Sound comes out of my speakers even when headphones are plugged in

This is probably an alsa issue. I had the same problem, but it got reported as a bug and fixed.

link to bug report

I had the same issue. It appears that the new kernel did not correctly detect the sound card model that you have. You will have to edit the /etc/modprobe.d/alsa-base.conf file and set the model manually with

options snd-hda-intel model=<model>

Unfortunately, finding the correct sound card model can take a little guess work. I took me several tries to find the sound card model that would detect the headphones correctly.

This link gives a list of sound card model: http://ubuntuforums.org/showthread.php?t=1043568

More information can be found on the Ubuntu Wiki.