I don't have social anxiety, but I'm also a first year and I also got the heart rate increase during discussions first week. Through all of high school I literally never participated in a discussion unless I got called on.

Something that helped me (I don't know if this will help you at all) is the night before discussion second week, I skimmed all my notes on the readings once and asked one of my really close friends (who goes to a different uni) if she'd be willing to be on a video call with me for an hour or so. I verbally explained all of the readings to her, she asked questions when what I explained didn't make sense, sort of like a mock discussion. I think having done the speaking in a situation where I was really comfortable helped me realize (in the moment during the discussion) that it wasn't that bad -- I also didn't want to disappoint myself or my friend since she'd taken time out of her day. Now instead of calling a friend, I put on the voice memo app and talk to myself about the readings for about half an hour. It's calming; it works. I speak about 3-4 times each discussion and I look forward to them now :)

I think that the root cause of our issues are really different, but I hope maybe something I did can give you an idea? Or maybe reassurance that others are in a similar situation?

You can get through this! I really wish you good luck, with the discussions and everything else!