When I was in undergrad doing premed work, it was a very intense and competitive, and I began experiencing some of the same things you've described, especially wrt anxiety during testing/exams. I immediately went to my university health center on campus and got in to see a psychiatrist. After evals and several appointments, my doc put me on Effexor, which is actually an antidepressant but is also used in anxiety. Whether it was placebo effect or genuine biochemical change, I was eventually able to eliminate the anxiety.
Of course, I am not suggesting this medication (or any other, for that matter) is right or wrong for you, and I don't want to get into a discussion about the pros and cons of medication use. However, my point is, it may be worth considering the psychiatry/medication route, alone or in conjunction with some form of therapy. My girlfriend is in a clinical psych program that does a lot of cognitive behavioral therapy (CBT).. something like that may also be beneficial.
As others have said, there are lots of options, and anxiety (and depression) is very treatable, generally. I had great success with my medication, and was able to stop taking it after about 2 years (again, this length of time will vary from one individual to another).
Consider your options and choose what you think is best. If it ends up not working out, try something else. Odds are you will be able to find some form of relief, in my opinion.
Good luck!