Most Helpful Girl
I think she is not your dream girl. Neither other one.
You cheated for whatever reason. Trust me it doesn't really matter.
You just feel guilty, because you realized it was wrong what you have done. You don't love her. You can't heal her pain. You can't build same trust. You are feeling lonely. But she is not your answer.
Let this girl go. She is about to create her own life. Let her. If you really love and respect her, let her be happy. Even it means your break up.
Don't do this again. It is not excuse to cheat. If you feel change in your partner, you ask, you don't cheat. This is how relationship works. There is no single reason for cheating. Such reason doesn't exist.