Sounds like you're parents are very controlling. I know a bunch of friends who go to school locally, and they still dorm there just to get that college experience. They only did it freshman year and met some friends, and now they live at home, but still hang with those people.
Try joining a club at school, if your SA isn't too bad. I find doing small things like that help the most with SA. Going to parties and bars can be overwhelming. Also, try joining a gym, or a book club. Whatever interests you. Remember, you don't need to throw yourself into highly anxiety causing situations. It is best to start small and work your way up.
