I agree with you in the thought that it sounds like an anxity disorder mixed with a form of depression. Just because someone has depression or and anxiety disorder they don't have to necessarily take meds. Sometimes just talking to a psychologist can do a lot to help. It sounds like your boyfriend has test anxiety which is a common thing at least in my college. I have done some research into this for one of my classes and despite the usual advice about studying in advance and gettting plenty of rest the night before I found out that if a person eats dark chocolate while taking a test it tends to calm their nerves which will help to aleviate the Test Anxiety.. I had a couple of my friends try this out whith out telling them what it was supposed to do and they said that they felt much better during the tests.. it was a controlled experiment that I implemented because i was curious about how accurate what i read was. Anyway it worked for them so maybe you could suggest this to your boyfriend. Going through depression yourself you may be able to help him out a little bit but I would suggest that he see a professional if things do not get better after talking to him. Also to help with his sensitivity have him go to a pyschologist because they can not prescribe medicine.. This may make him feel at least a little more comfortable.
Hope this Helps