Here is a thing I've learned about myself over the past couple of months.
When I am feeling self-conscious about social settings it is usually because I am being judgmental of other people - either in that situation or elsewhere in my life. When I deliberately stop judging people it is easier to stop worrying about what they think about me. And suddenly I have confidence to talk to other people and enjoy getting to know them. For some reason those two things are inseparably connected for me. And it is very freeing to spend time with other people and simply enjoy being friends.
So that is something I've been practicing. It sounds simple and obvious, but it is making a difference for me.