You should have a right to privacy in a relationship. All people should have. Your relationship is early on and people have things they aren't comfortable sharing yet, and that is okay. 

Her snooping through your things is a red flag. That really isn't okay. It doesn't matter if you are a private person. In a healthy relationship, communicating is important. If she has concerns, she should talk to you about them and hear you out. She can set boundaries and talk to you about what behaviors are cheating and you can agree where the relationship is. Building trust takes time and that is fine, but it doesn't give her any right to break your trust by looking through your stuff. If she doesn't fully trust you yet, the way to handle that would be taking the relationship slower and really getting to know you as a person. What she did is wrong. 

I don't know what happened in your past that you're hiding, and I really don't want to/need to, but it doesn't seem like it could be that bad if she saw and is still dating you and acting like nothing happened. So maybe that is some reassurance to you. I think you should ask her. If she admits it, who knows where it will go but it's better to face it and start your relationship on a more solid foundation. You can let her know you had some things happen to you when younger that you just aren't ready to talk to her about, but that you will when ready and she should respect that. She might respond to all of this harshly, but remember that says more about her. She is breaking your trust, invading your privacy, and also not being honest/communicating well. It's better to get it all out there now and handled. If the relationship doesn't work out, better to know before getting deeper into it. If it does work out, it can be stronger than ever going forward. 

All that aside, there are some hints here you may have gone through some significant stuff and I really hope that you are or will seek out help and support for yourself. Trauma never just fades away and it can have serious ramifications on your mental health, physical health, and behavior. You might not even realize. That doesn't mean you are hopeless of doomed by any means. But you do need to actually heal and not brush it aside.