Should you be worried if you've been with your girlfriend 4 months and recently her ex-crush chatted with her online and asked her out and your girlfriend said she was swayed by him but she apologized?

All of us like flattery and your girlfriend was simply flattered and probably remembered the "good old times" she had with her ex, but realized quickly why he is her ex. I wouldn't worry too much and she sounds like a confident young woman that at least admitted her feelings to you and then aplogized. However, tell her to stop the chatting online and you are a one woman man, and that's the way it is. Say it nicely, but make sure she knows the ground rules loud and clear. Good luck Marcy