Thanks for writing in, it isn't easy to confront these feelings.
You might not think it but anxiety can be conquered but you'll need various approaches to do so not just one. That's if you have anxiety, a proper diagnosis is needed with all illnesses otherwise you are guessing and just like a car mechanical issue you can renew lots of parts but not the right one if diagnosis isn't determined.
So your first point of call from here is your GP. Now, let's assume for the exercise that you have anxiety (but you could have other issues like mild OCD, social anxiety and depression for example, the other measures you can take include (click on the links but you only need to read the first post of each-
Distancing yourself from toxic people
Writing down feelings and plans
Discussion like here and with those you trust
Motivation from lectures, books and internet searches
Bit if reading there but education on these things is paramount. Finally, we cannot all "fit in" with other people. Those with social constraints are better off living on the rim of social circles and waiting for that connection with others for special trusting friendships. What occurred in class to embarrass you isn't unusual but us sensitive types take it to heart and the more you show your sensitivity the more they will ground you into the ground about it- sadly. If you take the mature approach and casually inform them they are childish and "I've forgotten about that, it doesn't worry me" then the tormenting will drift off.
Sensitive people must stand up and grow that thicker skin although it is really hard to do. Even if you appear to have grown that but are hurt internally- it is better than poor reaction of which they seek.
I hope I've helped.