I agree with Thumper. I think a person who cheats will cheat whether they're an alcoholic or not. A person who is faithful remains faithful even as a drunk.
I know people will blame being drunk -- and say things like "it didn't matter because I was so blacked out I didn't even know what was happening"... but that doesn't cut it for me. In a relationship where you care about and love the person you're with, you don't cheat no matter how drunk you get. It's a separate issue.
Now -- can a selfish person be both an alcoholic and a cheater? Absolutely.
I'm sorry you have to worry about this. I think it's important to remember in both cases that the three Cs cover cheating too (at least in my book) -- and nothing you did caused him to cheat.