I know how hard it can be to deal with social anxiety. Mine is pretty bad and it constantly makes my life more difficult. What I try to do, is remember that what triggers social anxiety in general is advanced fear of something before it actually happens - like switching schools, which is my case. So what we must do, is try to stop negative feelings before they actually begin to threaten us. Try to accept the fact that you don't know what's going to happen - and that the possibility of something bad happening is much smaller than the possibility of things running smoothly. And when you feel like people are staring at you and making comments about you - try to really focus on them and in your surroundings, instead of focusing solely on yourself. It makes you realize than people are usually too worried about their own lives to pay attention to you.
If you need to ask a question to your teacher during class, you can try to focus only on him or her. Pay attention to their words, not you your fellow classmates - that are probably going to be too busy gossiping to pay attention to your question anyways. Or you can simply make a subtle sign to your teacher to call him or her over, so you have more privacy and will feel more comfortable.
And less but not least, you can always talk to a therapist so they can help you to work with your issues and have a little more self-confidence. It's going to be just fine, I promise.
If you need to talk to someone, I'm always here for you :)