I can understand how she feels smothered. If you wanted to live together, why not find somewhere that you both want to live and somewhere you can both afford live in?
No one likes to feel like they are a charity case, and I suspect that is how the girlfriend feels (though obvioulsly you aren't intending it to be that way).
She feels that university is very important, and rightly so. She wants to do the best that she can do and for whatever reasons she doesn't believe that she can 100% commit to you.
You seem to be very different people and want different things, she seems slightly aloof (understandable as she is putting most of her effort/time/attention into her studies) whilst you are the very intense and keen boyfriend (which is also fine!).
Her wanting to move, no matter what, is very common and is quite mature and sensible. You trying to stop that is controlling and wrong.
Some time apart will do you both the world of good and will all you both to take stock and decide what the best course of action is.
Packing up and leaving everything seems a bit drastic at this moment, especially if you are doing it for the wrong reaons.