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I too am a former cheater, so I won't beat the OP that bad.
You're in emotional hell because you haven't accepted the fact that you hurt her just as bad as she hurt you right now.
My advice to you is this, tell her what you know about her cheating, and tell her about your own. Cheating is usually a sign that something is missing. Since you both are doing it, it's highly likely neither of you is getting all you want. Being honest with her makes the tables fair. From there you can decide if you want to determine what was missing that caused you both to seek stuff outside the relationship and figure out a way to make it better, or if you want to walk away now.
The other alternative, as suggested, is to recognize that you're already in an open relationship, and you can continue that way with the only new development being you both know it's an open relationship. But the way that it all came about, I'm doubtful this will work for you.
I support this opinion. IF you want to save the relationship (which is not the only or the best option here) you should admit your own cheating from the past. That way you'll be "even" (assuming you do feel even with her) and you won't be the "begging jealous partner", no, suddenly you'll have common ground. You both weren't as invested in the relationship as you thought you were. Your point seems to be that this was a mistake and you should have been faithful. If she thinks about her own part in it the same way you might actually have a chance to move on from this.
Word of warning, if you don't confess your own cheating that means even if she gets her shit back together (for a while) there's still going to be that disconnect between you two. And guess what, that disconnect is the reason for BOTH of your cheating. Slapping a patch on this won't work, you need to "start over".