Yes, that is a very tough one. There is probably a lot of work ahead for you; I'd suggest therapy at least. I fell in love with someone besides my wife and realized through it that I want to have children (my wife does not), so I have a little experience in that field. It's utterly awful, and I contemplate suicide every morning.
However, cheating does not in itself make you a bad person. Messed up, probably, but just because you made this big mistake doesn't mean you have ruined everything in your life. I know it is hard to keep perspective on that, especially if the suicidal thoughts are saying that you are worthless, but please hang in there long enough to heal. You may feel you don't deserve to live (I get that a lot), and that's ultimately up to you to decide I guess, but it takes some time to heal enough to clear your head.
Also, not that you necessarily want my advice, but you should probably tell your wife about it, sooner rather than later.