I don't think it is okay for your GF to treat you that way. Either she needs to change or you should probably walk. Unless this friend encourages you or enables you to harm yourself, there doesn't seem that there can be good reason for her behavior other than she wants to control you. If she were a man and you were a woman, it would send up the immediate red flags of an abusive relationship. (Actually, that is me making assumptions. Perhaps you are a girl with a girl.) Either way, whoever does it it is somewhat abusive to tell a person who they can speak to, and that kind of extreme jealousy, so early in the relationship is far from a good sign. It will likely only get worse.