Hi Ben, welcome to SR, I'm glad to hear you're using the chat room here.
I was very anti-social in early recovery, and for most of my drinking career I used alcohol to get me past those fears, I think it's a pretty common trait among alcoholics.
To get past it I had to force myself to look people in the eye, and to hold out my hand and introduce myself. One thing that has helped me immensely is to be a greeter once a week at AA meetings, I've been doing that for 4 years now. And the funniest thing, when I hold my hand out and say hello, or smile at someone, usually they're very friendly in return.