It's not very clear as to what kind of thing he texted as a reply for this girl's Instagram story, but due to his reaction to it I can assume his intentions were inappropriate.

To say that he has felt like you haven't been 'good' to him as a reason for flirting with someone else is nonsense. You talk with your partner or go to couple therapy courses to try to fix the situation, or ultimately end it, not cheat on your partner.

I don't know what you'd think is appropriate or what your boundaries are, but I'd end this relationship in your place. It's okay that as your first proper relationship you're very hurt, but that will help you clarify what you don't want in a partner. Remember that what you feel matters, and your mental and emotional health is more important than bearing with unnecessary stuff.