First I cheated, then she cheated on me. Now we're stuck.
Wow, that sounds like a rough situation. Did she know you cheated when she decided to cheat?
No, she didn't know anything about it.
It sounds like both of you need to sit down and talk out why you are cheating on each other. You may find out that a simple conversation clears the air and your guilt.
I don't know if that's going to work.
You might not be able to talk it out, but you'll never know until you try. If you want to stay in the relationship, I think you need to do it.