The only class I've taken as a psych major that's directly addressed social anxiety is psychopharmacology, a class on drugs that act on the brain basically. I thought that class was very informative. Abnormal psych and clinical psych probably also address SA, but these are not areas of interest to me.
As far as understanding myself goes... I guess I'm not sure quite what that means. Why do I do what I do? How did I get to be who I am? I guess these questions never really needed to be answered by psychology. Really, these questions never really need to be answered ever. What I would say to you, though, is that if you are curious about why you do the things you do, psychology will offer you a "perspective" on yourself, mostly via what it says about large groups of people that you happen to fall into.