I think you’ve blown this one. The problem you appear to have is impulse control and lack of maturity. 😳 (Sorry, but it’s true!) You put your own needs ahead of hers, and it’s impossible to have a relationship when someone who needs sex and isn’t getting it enough, decides to cheat to feel good, rather than work things out within the relationship. You didn’t really say why your intimacy with your girlfriend plummeted, so I’m guessing it was a normal slump. But your inability to communicate with her and make your sex life come alive again with her is going to be a deal breaker for ANY woman you’re involved with long term.
Until you deal with this problem that you term as “needy”, and she can see you’ve changed, I don’t think you can get her back. 🙁