2 weeks ago my LTR told me she contacted a guy from her town because he was sick and went through a surgery. Now I found out they have been texting each other since. I saw the the texts and she also talked about me, about my birthday, that she was lucky for having me, so I don't think it was that bad but in general she seemed to be having fun talking with him. At one point the guy asked her out on a date and she refused. The thing is that he was clearly hitting on her and she kept talking with him. I told her that I can't accept that and she immediately blocked him and begged me to not leave her. What's the correct move here?

EDIT: Thanks for all the insight guys, I read all the replies and I think I'm going to keep her and proceed with caution while focusing on getting plates