Is it ok for an applied mathematician to research a topic that she has personal experience with?

I do not have experience with specifically applied maths, but in general, there is no problem at all with conducting research in a direction that you have some personal connection with. One could argue that many applied research projects are driven by concrete needs, and I fail to see why those would have to be needs of other people rather than a researcher's own.

That being said, you will need to remain cautious of your own bias in your endeavours. As a researcher, it will be expected of you to work on the topic from a neutral, scientific, "big picture" perspective, which is easy to lose if you are at the same time also part of this "picture".

Let me provide one example from my own research. I conduct research on software engineering. Many of our best PhD students have worked as software developers prior to starting their PhD, so in a way they are also part of the same demographics that they research. What can now happen with inexperienced students is that (s)he will, for instance, interview developers with regard to a specific problem, process, or practice, and, during the analysis phase, discard statements that go against their own prior experience as "obviously wrong" or "bad". In that way, a student may overemphasize results that resonate with her/his own prior experience, and discard results that don't, essentially guaranteeing that the results are in line with what the student expected going into the study based on her/his own experience.

You will need to make sure that you do not run into the same trap - don't assume that everybody experiences your health issues the same way, that you are some sort of gold standard of this specific condition, or that your specific variation is more important or relevant than others. However, these are definitely issues that a good advisor can help you with.

Having personal engagement with your research can be a great benefit:

• Being directly affected by something is a strong motivator for persisting through the inevitable struggles of research.
• Being engaged also gives you perspective that may help with formulating effective questions and answers and avoiding traps in thinking.

Some successful examples I personally know in the biomedical field include an amputee researcher of artificial limbs and an autism researcher with an autistic sibling.

As @xLeitix says, there can be challenges with personal bias, but I don't see that as any different than the personal bias that all researchers bring to their subjects.

In fact, I think one needs to be more careful if you are not directly engaged with a problem, because it is easy to be blind to the true needs of the people involved. Consider, for example, the way in which a largely male medical establishment simply ignored many aspects of women's health for many years, or the continuing embarrassment of many misguided aid projects in the developing world.

In short: go where your passion is taking you.