OK. Having some experience with social anxiety I might be able to offer some advice. First step, go to doctors and make sure that there is nothing physically wrong with you. Can I ask, are your symptoms the result of over-breathing?
Doctor should have told you how to deal with a panic attack. Either sit down (upright) in a chair and proceed to take long, deep breaths until you feel better. Or, distract yourself. Look around you and put your mind to something else. Talk to someone about something, anything; eventually you'll feel better.
Knowing how to deal with a panic attack, if you didn't already know, will make you feel much safer.
On to the social anxiety. The crux of the problem is that you have unrealisically negative views about yourself. What you need to do is think carefully about the kind of things that you worry about. It might help if you do this with a close friend. For example, when reading out your work, what would be the worst thing that could happen? At the very worst, people would laugh at you and you would go red. Imagine that someone else in the class had their work read out and it was truly awful stuff. You would laugh them, sure. But would it really matter? Would your opinion of this person change? Have you ever laughed at anyone else's mistakes or stumblings? Of course you have. Our mistakes, as much as our successes, go to make us who we are. I suppose it comes down to accepting yourself. Think to yourself that, with what you have acheived so far, even if you don't progress any further, you will still have done better than the average guy off the street. Instead of consuming yourself with worry about who you are and whether people will like or accept you, live your life how you wish and remember that however you live it there will always be some people who love and value you for it.