I have been trusting enough of my SO to leave my personal belongings out and about, and without fail, he goes through it every time. Then he gets pissed off at me when I'm venting in my journal. This has happened so often now that it comes down to how sneaky can I be, where can I hide it, so that he doesn't catch me venting, doesn't get mad at me, and then we have no problems.
So, trust works both ways. No, you're not wrong to want to keep something private. Just try to find a rational way to communicate this to her. If she can't accept that, well, it's up to you to decide if this is something you can compromise on, if you're willing to work on it, or if it's a deal buster.
Also, two months isn't exactly a ridiculous amount of time in which to learn to trust one another, which explains why you freaked out instead of rationally explaining your point of view, and maybe also why she went through your phone.