I am going to pipe in with the obvious alternative... if a marriage isn't working, get a divorce. The great thing about divorce is that it ends these difficult struggles. You will be free to have sex with other people. And, you will do your own housework without the need to please anyone but yourself.
Marriage without sex is ridiculous... there is a big difference between monogamy and abstinence. If you need to earn sex by doing housework, that isn't a fun way to live. That you are thinking so much about having an affair indicates that the marriage isn't working for you.
I have never had an affair... so I can't speak to that. I will say that I have been much happier since my divorce.