Accept the breakup — Stop pestering your ex to change their decision. - Accept responsibility — Stop blaming others. - Pay For What You've Done — It is very.
My girlfriend cheated on me too (an ex did) so I know exactly what you're going through. It's a truly horrible situation to be in. The thing is, it's already happened.
If you have no intention of marrying this girl, break up with her. Not to slink back to your ex, but to free your current girlfriend to find the man who wants to marry her.