Being Muslim and antisocial

I'm very antisocial, I get very anxious when I meet new people and I don't like having to deal with annoying people and I tend to get really upset and overthink about how people see me. I want to know if there is some ruling regarding ignoring people or not being friendly and approachable

You are not required to be more social than you want to be. As long as you are polite and dutiful toward your relatives when necessary, then you are free to avoid interacting too much people with people.