Hello Katie and welcome to the forum and soon to Switzerland.
You have the right attitude, you should definitely make friends on your own, instead of relying 100% on your boyfriends friends, you'll need someone to talk to when he's not behaving, right?
I honestly don't know many expats that young here in Basel, I know many late 20's / early 30's but I guess a lot of things depends on what your plans are? Go to school, go to work? I'm sure you'll meet plenty of new people your age if you get to school.