I agree. Huh? And your girlfriend is punishing you by withholding sex?
The problem is not that you talked about the old days with an old friend. The problem is that the two of you aren’t talking about what you really need to be talking about.
It isn’t helpful to argue with her about whether you should or should not apologize. It would be much more useful to address the basis of her insecurity directly. I can’t tell from your letter if she is overly anxious and jealous or if there is something you may be doing, however unintentionally, that is making her feel vulnerable. On the face of it, this incident is innocent and she is over-reacting. But it may be that there has been a build up of incidents and that this one was some kind of “last straw.”
I am guessing you are in the early stages of a relationship. It’s important for the two of you to have a conversation about the basis of her concern and to work it through. You are setting the foundation for how you will relate to each other in the future.
I wish you well.