As for class discussions and debates, what I always did was overprepare. I prepared every possible point and rebuttal I could think of. That way, it’s very very easy to make connections to what other people are saying so it’s not too hard to come up with a response because I already came up with it the night before. I will say being able to make “connections” is a skill you develop from critical thinking and being able to analyze text or whatever. Getting a word in edgewise you kind of have to be ready to speak right away before someone else speaks up, which is what I had the most trouble with. Have you told your professors about your social anxiety? The university should be able to accommodate if you provide proof of diagnosis.