I believe that despite having an opinion, the options are always still up to you. It does take a lot to realize that you have made a mistake, and you did, and you own up to it by being able to admit it maturely. You have to understand that she does have reason to doubt you, and that's also okay, but I do think that no matter how much you love her, you didn't love her enough to stay completely faithful. You are partially to blame for the mistake, but you're also human, and it happens a lot. Of course it's wrong, but you are learning from it right now through her, though it is unfortunate that she had to be the one to deal with it.
I think that it's probably time to consider ending the relationship, because no relationship is healthy if it's with constant doubting and fretting over what's right or wrong to do. Of course, you should be mature and talk it out with her, and maybe things will change, but I you're unwilling to even communicate, then it is time to consider the end of it. You are both at fault for the downsides of it, and if it's too much to take, then you're better off with different people.