The college experience is entirely unique. You'll be a little homesick here and there, which is totally normal!! It's a new environment and something you've never had to experience before, so it's completely normal to be nervous, sad, scared, or any sort of uncomfortable about the situation. However, there are things you can do to make it a little easier. Make good friends, attend on-campus events, take care of yourself. Have fun, really! If you're occupied with things that make you happier, you'll be less focused on the things that are making you homesick. As for not having an "adult" around, well, you are the adult now. I know it sounds daunting and boring but remember to be careful, make good decisions, and listen to your gut if a situation doesn't feel right.
I'm in my third year of college, and I'm totally down to answer any questions you might have!! Our experiences might not be exactly the same, but I'm happy to help if I can :)