Just Can't Shake the Guilt...

Got divorced a month ago after six years of marriage. Thought we were solid, but she wanted kids and I didn't. We tried for years to agree on something else, but nothing stuck. In that last year, though, before all this came out, I started sneaking around with one of my co-workers. She's married too, so it was always discreet, quick affairs in the back parking lot or hotel rooms. Now everything is falling apart and I feel terrible about it. Guilt eats at me day and night. Should I come clean to her now? Is it normal to want to confess even when I know she shouldn't find out?