You and she both seem to have trust issues. How can she trust you if you don't trust her? How can you trust her if she can't trust you? It's a vicious cycle.

From experiencing a long distance relationship, I found that it is harder to keep trust when you don't see your significant other often. There is no personal connection. Phone calls and instant messages don't create that.

I do not see pursuing this relationship as a good idea. I think it would be good for you to take a break away from it and think about other things.