Welcome to the forum, Emily. As you can see there is no lack of advice and much of it well considered. On the flip side though only you have the personal contact and experience to decide what path to follow.
However, once the trust has been fractured it becomes very hard to recover trust, but it can be done. I agree with the group that says you should exercise great caution. It appears to me that you don't really know each other at the deep level. You should not have searched her phone but what you found was that she was doing things that can be hurtful to you. It is great that she is accepting of your dressing, but the larger question seems to be why is she accepting? It seems to me it may be for purposes other than forming a comfortable relationship.
What should you do? I really can't say because I don't know her side or know her. But it does seem to be a time to be extra cautious. Perhaps it is time to stay away from serious relationships as breaking up from a marriage that ended badly can produce some deep trauma. That can take awhile to heal. But being in a relationship with this new woman where there are secretive things going on seems to me might be adding to your own hurts from the failed marriage, that is, you may be vulnerable to further injury. Unfortunately, it is very difficult for any of us to say what should happen because we don't really know the whole story. But the advice provided here is good in general, although quite variable because we don't know the whole situation.
I think if you are a part of this forum you may find some healing and support which is needed to help you over this period of difficulty. Some here have had similar relationship histories as you have.