YAY a topic I can weigh in on.
Cheating is very easy to define. when you do something you feel you need to hide from your partner.
that is what cheating is.
for some people a flirty message is cheating.
if the rules for cheating in a relationship were 100% set in stone no relationships would ever work.
for me and my SO, that would not be cheating at all, we would laugh it off 100%.
however, if I were to do something with another girl and hide what I was doing from my SO, that would be cheating. even if it were a peck on the cheek. its not so much the action as the lie about it.
OP in your case, she did not hide it, you knew about it, and you could speak about it like an adult, what is the issue? if you got angry, and it all started a fight then maybe you should not be in a relationship with anyone until you can trust yourself***
***lots of missing context here, a fight where people get angry is fine, but if you ever look back and say to yourself, you know what, maybe I was out of line and I should not have said those things, then trust me, get yourself in order before you get to your next relationship first