Any place for people with fear of writing?
I do resonate with your experience because I was scared to write (English is not my mother tongue) and I am also an introvert. I have been reading much about writing and networking and here are some tried and working methods (by me) that I wish will also help you. In the case of real fear, I agree that talking to some professional will also be advisable.
Don't "write," instead, draft then edit
My biggest "A-ha--!" moment was learning that most writers don't really write a perfect sentence at the first go, instead, they draft and edit. And for me, my mind has eased up so much once I have learned this distinction and decided to split my writing tasks into drafting and editing. In drafting, I just freely interpret the data and plug in some discussion here and there, occasionally with some anecdotes, etc. I never edit them. Then, after a couple days, I return to edit the piece. On a good day, I got to keep about 40-60% of them; on a bad day, I may have to slash 80-90%, but also often have a good laugh at what I wrote.
This finding really liberated me. I'd suggest you give this a try as well.
Write to think instead of think to write
Instead of writing to tell people what you think, I found it easier to write it as if I am having a discussion with myself. I wrote the research question, and then gave some answers, and then went back to question the answers more. I was often surprised that many times I read the scribble and figured out "Oh, this is what it is!"
I would advise against crafting out a perfect sentence and then put it on paper. This is futile because mind works a lot faster and non-linear than typing/writing process. By the time a "perfect" sentence is written, a lot of useful thoughts might have been suppressed or forgotten.
Dedicate times to write
Silvia in How to Write a Lot introduces a method that involves making a time and a space to write. I adopted the method this way: I block out time a few weeks ahead as writing/analysis time, then I guard that time. I cleared up the wall and the desk I face when I work on the computer so that I can only see the computer (and other books/articles I use) when I write. There is no picture, stationery, picture frame, etc. 120 degrees in front of my eyes. I also close down e-mail, silent my phone, and close the door.
Boice in Professors as Writers: A Self-Help Guide to Productive Writing even goes so far to suggest coupling important and crucial daily ritual (such as shower) with writing hour. No writing? No shower. I found this kind of stressful, but perhaps may work for people with a different personality.
Document time as well as words
Productivity aside, it's more fulfilling to document my writing effort in both time and output. High output is, of course, great. But I have also come to realize that reminding myself I have been dedicating a fixed time regularly to write, albeit slow and low, makes me feel more confident.
Free writing
Goodson in Becoming an Academic Writer explains some pretty nice workshops to foster a healthy writing habit. The starting one is to "free write." Free writing is not new, and some people use this to warm up or tune into the internal writer channel. It's really simple, just sit down, open an blank document, minimize the visible area so that you cannot see what you type, set a time limit, and pour out all sorts of thought that goes inside your mind. Anything, just type.
Usually, after the time limit (I started with 5, now 10,) you'll have a pretty clutter-free mind and clearer idea on what that day's writing is gonna be.
Use proxy of writing
There are many, many ways one can put down an idea without initially writing it out. Drawing a mind map, popularized by Buzan, can help forming a bird view of an article. Paper and colored pen are good enough, online tools such as VUE are abundant.
Doodling, such as Sketchnote recommended by Rohde, can also be a fun way to "play" with words and idea.
For scientific writing, a paper by O'Coonor and Holmquist in 2009 suggests a pretty interesting method: basing your writing on a key output, such as a graph of the results, or a table of an analysis, and then build from there. For most experienced researchers this may be nearly common sense, but for those who think a paper should be written from Abstract to Conclusion linearly, this paper would help re-orienting them. My former supervisor, knowing my hesitation for writing, actually used this very method when advising me.
Use a recorder to document your thoughts or use speech recognition software to dictate your spoken words into texts may also help you break away from the deep-rooted fear towards writing.
Harness creativity
When writing output falls, I feel tired. After some trials and errors, I figured out that I feel tried not because I lacked energy, but because of too much creative thoughts didn't get to be expressed. So, I play music, pick a challenging recipe and make a potentially horrible dish (and eat it, butter + pepper + red wine always save the day), play LEGO, knit and crochet, come to answer questions... etc. I actually picked up a lot of habits through my doctoral study.
Introvert vs. extrovert
Being an introvert is actually not bad! In most modern culture extroverts get a lot more praises and attentions, but if you cast a critical look at it, this world needs both types to run properly. Two books I read last year were quite inspiring: Zack's Networking for People Who Hate Networking provides advices on how to focus your energy and properly carry out quality networking; Laney's The Introvert Advantage provides a more holistic look at how extroverts and introverts work, and how to cope and thrive as an introvert.
Closing remark
Best of luck and, really, enjoy the ride even it's scary. After the PhD thesis, there will be more collaboration and you will not feel as lonely. When I am down and want some healing reading, I often flip through Lamott's Bird by Bird and Zinsser's On Writing Well. They are also a good choice before reading those more serious and pragmatic how-to guides on writing.
Whenever I feel cognitively/academically inferior/inappropriate, I would think about a remark of Florence Foster Jenkins, who slaughtered Mozart's Queen of the Night aria (Try listen to Edda Moser's version first, and then Jenkin's version): "People may say I can't sing, but no one can ever say I didn't sing." Before worrying doing it well, do it first, and you will improve.
The fact is I have never met one person in my life who genuinely embraces writing as if they "love" to write. Most successful writers, when interviewed, often just say things like "What tips? I just write," or "I draft, and then I write, rewrite, and then I rewrite again." Betty's Drawing on the Right Side of the Brain has made a lot of people realize they can draw; I wish there will be a book called Writing on the Right Side of the Brain that will make people realize that we all can write, but we probably have to wait until the neuroscientists get over their fear of writing.
The only thing you should do is to seek professional advice. Writer's block (in all its forms) is not uncommon and it is clearly possible to remedy. I cannot and will not get into possible reasons for why this occurs but clearly in a PhD, particularly early on, it may seem like a daunting affair. To avoid ones problems is not the solution. If you see yourself in academic jobs (in or outside academia) writing will be one of your main tools. To try to find a job where this is not necessary will be difficult unless you see yourself switching direction completely. So the advice is seek help now. You will not be the first one to do so and will not be the first who will be able to continue.
It is your PHD. You have to write. Papers, reports, thesis. It cannot be done otherwise. On the other hand, you must know that all of us have collapsed (or constantly collapsing) under pressure, one way or another. Others have stayed in bed not wanting to get up. Others blocked out and could not perform. The "stronger" ones sucked it all in (externally) and developed serious health issues. So, you are not alone.
You should fight it. Get a girlfriend / boyfriend. Talk to your family and friends. Exercise, do sports. As wiser people have said "Whatever it takes to keep your hands free". But even then, you might not be able to fight it alone and might need to seek some professional help. It is not a shame. It is actually a brave action to admit you are not always strong in a world full of hypocrites and wannabes.
In term of practical advice. Select some successful authors in your research area that you really like their writing style. In the beginning, partially emulate their style. See how they describe the challenges and the related work. Rephrase the related paragraphs in your unique style. Then add in your what are you trying to do. That will be enough to make it through the introduction and the related work. Beginning is always the hardest part. Once those 1-3 pages are out of the way and you start to write "your" contribution and "your" experiments, you will see that things get easier. So, in the beginning emulate and adapt (but not copy) from the authors you like. After 1-2 written papers, you will see that you do not need to do that anymore and you have developed your style. Most of all, enjoy the process. Everyone has gone through your phase and you CAN and WILL get through it.