You guys are missing one very important factor: Honesty. You don't want to explain to her that she's been invading your space and privacy, in case she takes it the wrong way, that's not healthy, if something is bothering you, you should be able to honestly explain your feelings without fear.
Her actions, however, seem to display distrust in you. Everyone needs space and time to accomplish individual tasks. We as human beings cannot be glued to our phones or other people, that again would not be healthy.
Is there a specific reason she is acting this way? Is there a lack of affirmation?
I would not resort to a break-up just yet IF you see a future with this girl. The two of you desperately need an open and honest conversation about both your emotions lately.