I very much relate to this. I am one of those that cannot even handle a drink or two at all without cycling big time. It's really hard when social events come up as I already am shy and don't feel I fit in.
I don't have any real friends here where I live, and am on disability which cuts me off socially. But you sound like you still have some friends and that's a good start. Maybe you could try just very slowly and make each time a little longer, then closer together.
Good luck!!