Think about what Pook said about how it is natural for the bird to want to be free, and it is unnatural for the bird to fly willingly into the cage. You have been caged and its going against your true nature. The cage of course is a monogamous relationship and all the expectations that come with it.
Your solution is to redefine the terms of the relationship to one that suits you better, and that is on YOUR terms, not hers. She is of course free to refuse and end your relationship. But you don't have to be bf/gf "just because that's how everyone else does it". You're free to define what "relationship" means to you.
This is what happens when you get better with women... you think the goal is to get a girlfriend, but what you end up realizing is that the process of meeting new people and having unique experiences is really what makes you feel the best inside. You were under the faulty assumption that having a girlfriend was the goal when you had a scarcity mentality, now with an abundance mentality you realize, not having a girlfriend is the goal!
There's an "abundance" of amazing people and experiences out there, and you don't want to miss out on them. This is what's known as a "good problem" to have. Good luck.
BTW there's really nothing PUA about your situation. This is the oldest story in the world.