Your reactions that you mentioned as bullet points seem to be signs of insecurity. One thing to remember about insecurity is that while those you talk about appear to be confident about a certain thing, they can't be confident or good at everything. There are things that you're better at than they are. We are all different with different qualities we can bring to the picture. Sometimes what we're really good at is not relevant in work situations. (e.g. I might be a great cook while working at a finance firm...)

Instead of letting yourself feel insecure and competitive (and angry) as a result, try to bring something unique and different of your own to the table when you meet (maybe a different angle to look at things?). And again, it's no point worrying about how you are perceived especially at the moment as you are dealing with the anxiety. You need to give yourself some slack. Once you're better, you can focus on how you're perceived more.

Generally, try to push through while letting the anxiety be there and inviting it more but not focusing on it.

Good luck!