Better to be heartbroken and free, than be “loved” and chained
Very rarely do I advocate quick breakups, as I believe many relationships often just need a little tweaking, but you don’t want to be with someone like this. If you really care for this girl, I suggest telling her (in a nice way) that how she is behaving says that she’s insecure about the situation. You can ask her why that is. If she does not behave rationally, and she continues to behave this way, cut it off. Entirely.
Don’t set a completely unreasonable precedent if you want this relationship to end up healthy
You don’t have to be ugly about it all, but you also can’t let another person control your friendships, hours and communications, which is what someone like this will likely want eventually.