It goes alot further than child support. You will be miserable (especially later on) if you can't be a part of you child's life. And even WORSE, that child needs you ..... his/her life can be totally changed without you in their life.
I can see both sides of the story. If you tell her you're cheating on her, you may not have a chance EVER again and may not be a part of their lives. On the other hand (not telling her), you may live with a feeling of guilt .... and in the case that she DOES find out (the hard way), you're stuck again. I would have to say that it really depends on the kind of person she is.
Scenario: You tell her what you've done, that you've changed into a different person, you're sorry, and you'll never do it again.
Only you know her. Would she freak out on you and say thats it? Or would she possibly understand and trust you? It would take a really strong (or dumb, no offense) person to do the latter. But hopefully she would (for the child's sake). If you think she WOULD freak out and say no more ..... I would just make sure the other girl is ditched FOR GOOD, never think about it again .... pretend it didn't happen & hope for the best. Oh, and think with the right head from there on. What you did was wrong (I'm sure you know that, though) & hopefully you learned from that.