There is a phrase used to threaten in the context of a conflict. In media, you might hear people exchange with:
However, these are words that are exchanged when direct, maybe physical, conflict is bound to occur.
In the case of your example, I'm afraid that doesn't work as well. At least from my understanding, you can just skip over that and ask why they did that action with a very direct tone, and that will get the point across. Contrast these two reply examples:
But those were also my pictures. (lit. There were also pictures of mine there)
raising a passive complaint
Why did you toss them?! Those pictures were also mine!
people generally avoid direct confrontation, so directly calling out an action already carries the feel of saying "What's your problem?" without saying it.
You could really emphasize it by ending your sentence with some sort of emphatic remark like おかしいよ、君。 This remark might actually be the "What's your problem?" that you're looking for, but it doesn't mean that in a literal sense, however. The phrase does not translate well into Japanese.
EDIT: Thanks to Chocolate and l'électeur (as usual) for the assist.