What is my girlfriend ? really saying here ?

Lets be real here,You know and I know, after reading your story that this relationship is doomed. The might be great but there is a hell of a lot more to a relationship and right at the top of the list is communication. Its only been just over 3 months and already you are frustrated. Stay friends or part now. While you are still with her (and not that happy) you are wasting time when you could be meeting someone else. Good luck with that.