I would come completely clean to both her, and the other girl. Your avoidance of pushing the other girl completely away, is like leaving the back door open. It would read that way to your girlfriend who saw the messages also. They call those EAs or emotional affairs. I believe you never meant to cheat, and physically you did not. The more you come clean to her and see her point of view the more chance you have. The problem with dating is nobody is fully vested in the relationship. It may be hard to fix after this.