Every case of AS is different. My son is 5, and he loves to go places, and is very social with adults, just not with children his age. He definitely does not seem as anxious as you described your childhood. He has an excellent memory, but so far he does not appear to be gifted. He never banged his head or bit himself, but he does flap his hands. He is obsessed with makes and models of cars. My son was a very late walker (21 mos) He had speech at the normal time, but was not using it in back and forth conversation.
Did you have any speech difficulties? That is often a clue, but not always. Like I said, every case is different, but the way you describe yourself does sound like many of the cases of AS that I have read about.