My boyfriend has been liking this other girl's photos?

[Joel]

Because of the "her" this he said, it could mean two things. One, he really is genuinely annoyed by her and took the picture with you to make A point. But, given the other evidence you presented, it seems like, in his spare time, he might be flirting with her and other girls possibly. I'm not saying it's a definite, but it's possible.

Ask him nicely, don't raise your voice and if he says something you don't like, reply calmly. "Babe do you ever flirt back with her?" Or something of the sort. That's how my girlfriend and I solve our problems and we haven't had a fight since we started using that method. We've been together almost 5 years now! Hope everything works out between y'all.