I think the OP wasn't exactly on the topic of cheating at all and this has become kind of a sub-discussion within the "marriage" one -- however, I was responding to your previous post where you said that "unlike men" you were monogamous. The truth is both men and women have to go against their natural inclinations to be truly monogamous. And I am not looking to be argumentative with you about whether you are or you aren't (since I wouldn't know anyway). I do, however, know many women who have told me they are monogamous or "they would never cheat" (a favorite) but partake in the monkey-branching I described with a man (or men) they are interested in during the relationship. Again, that isn't monogamous. That is just making a preemptive strike.
We all people, regardless of our sex, have an inclination towards sin. Towards self destruction through sin even. Some of us have a stronger inclination, some a lesser one. Cheating is a part of this inclination.
But at the same time, we as people have this great gift called "free will". And this dictates how we live and also how we die.
Another thing that is affected by our free will is how people perceive us. This is why @OP is in this situation.
In this life, people will keep judging you by your actions. And it's as fair as things can be. Most of us will struggle in this battle between morality and sin until the day we die. And all the best of us can do is keep fighting, striving to become our best selves.
As to the OP I totally ignored so far, I feel like you don't know what to do because you don't know what you want. Look yourself in the metaphorical mirror and really think about it. If you want to be with her, all you can do is being honest. God knows if she can ever feel the same again with you, but you do your part. If what you want is to get away, say a nice goodbye and be on your way. In the end, in both situation the best thing to do is to be honest (with yourself and with her).