If she is willing to breakup with you for anything at all, even a small mistake, I'd SWIFTLY move the fuck on.

That with other things you've mentioned makes me think she does it to control you, other wording would be manipulation.

Her showing you her texts, for one doesn't mean she couldn't delete things, or alter them entirely to look okay, but it also opens the door for her to casually ask to see yours, which isn't fair. If ANYONE asks to read your shit or have your phone in general they themselves are unhappy and are wanting to find a reason to justify it, without actually realizing they're just unhappy cause THEY are unhappy.

Not saying what you did is okay, but like others said you're young and honestly that isn't much to harm a relationship tbh, an apology and saying what went down should be enough to trust you that you aren't like that, if she ain't gunna trust ya ehhhh I'd move on, she seems very manipulative and controlling which can be yikes, as your needs will most likely be second to hers period.