*Sigh,* I was actually holding my breath when I read your post hoping that you would still say you never slept with her... *sigh*.... ah well, now you've gone and cheated. now what.
Well, for starters I will say what I always say and that is to do a tag search for "cheating" and you will see what hardships people go through as cheaters and being cheated on... even people that are the ones who cheat because the one that they were with cheated.
To me cheating is not ever an option, regardless of how much someone is dying to fuck, and says that their partner won't mind. To me, the go ahead comes from the partner, not the person I would want to sleep with. From experience I have learned that sex without full consent from all involved is just not worth it for the very reasons you are now experiencing. It's all hot and heavy and awesome during and then all hell sets in and people rise above hormones and suddenly "see" properly.
By how she is acting, she thinks she has fucked up. The man she is engaged to would not of liked what she did, by her thoughts and gut feeling. I would wonder if she told him or mentioned that you and her are getting to that point. I would wonder how much honesty she has had with him and also you for that matter... you only have her word after all as it seems you didn't contact him in advance....
She promised herself to another man. Whether he said to her or not that she should go and do whatever still doesn't indicate that he thought she would or that they set up some kind of way of dealing with that.... its all just words by the sounds of it. Or has she done this before.
It sounds like what usually happens happened.... sex changes EVERYTHING. I have never known in my own life for this to ever be different from this statement.
I have friends that would argue that point as they can fuck whomever and be kinda *meh, that was good* and move on... granted these experiences are more when they go to organized sex parties (swinging) or on dates with friends with benefits where EVERYONE knows what the nature of the relationship is, including their partners. I can see how sex wouldn't change everything when there is honesty and consideration, respect and foresight. It seems you two did not have any of this before having sex.
Where it does change everything for me is emotionally. Once its done, its done. There is no going back from those emotions. Granted it is different for others though. Hence the reason I pick very well when sex will happen with another.
These two things; everything not being above board and the emotions involved mean that nine times out of ten, sex changes everything. That is my point of view anyway.
It sounds like you learned something there.... not anything new really, not that I want to make light of it, but at 41, I have seen this similar situation played out many times for me and others, from the time I had my first experience until now... the idea is to LEARN from it. You were on the right track and then fell off of it as far as I'm concerned. Now its time to get back on with integrity and in humbleness. Stand up and apologize to this man and her and start doing what it is that will make you confident and honourable again. That doesn't mean that you have to end it with her, just be more mindful of what you want and of what is respectful to them.
I think if I were in your position now you could go a few ways; say good bye and leave her alone would be the first option. Secondly, discuss with her what she means to you and what you mean to her and then ask her to tell her fiance... then I would arrange to talk to him also. Maybe you could both tell him together. Then work towards an open and honest relationship with full disclosure and communication with him added. Thirdly, tell him and then chalk this up to experience. Tell him that you intend to keep your distance and not touch her again.