It seems to me that you and your girlfriend have not worked out what kind of relationship you both want. When the boundaries are unspoken there is a lot of room for misunderstanding, isn't there?
You can ask her about the messages. Was this just online flirting? Was it someone serious? Do you need to have an honesty agreement -- an understanding that before any personal meeting occurs you will let each other know about the third person and talk together about it?
In my opinion you can't just let it ride and expect any relationship to find its way by itself. One of the poly mantras is "communicate, communicate, communicate" and that should go for any open relationship. Heck, ANY relationship at all.
So talk to her. And write back with questions.