I would try not to worry, when first meeting anyone, about further down the line. I would practice being friendly to everyone, chatting with grocery clerks while I check out (about the weather or some piece of news everyone is talking about) and become friendly with the mail person and other service people who come to your parents home. I'd maybe join a couple support groups; one for myself and one for care-givers so you could be around other people who are more likely to understand what is going on with you and with whom you could "practice" sharing yourself until you're a bit more comfortable.

Do you go to class at your university (or is it online like mine)? Talk to fellow students, men and women; just becoming friends with others is the first step I think.