> -どうしましたか。
>
> -せきが出ます。

Apparently, this is a dialogue between a doctor and a patient. The doctor
says, " **What is the problem?** " and the patient answers, "I have a cough."

How could we naturally say " **what is your problem?** " talking to a person
who is acting strange? (What's your problem? - used for asking someone in a
threatening way why they are behaving in a way that you do not like or approve
of (Macmillan Dictionary)). For example:

> I have thrown away all the old photographs. - What's your problem? Those
> were my photos too!
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expressions slang
What's your problem? in Japanese
There is a phrase used to threaten in the context of a conflict. In media, you
might hear people exchange with:

> どうした？文句｛もんく｝あるのか。

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:

> **Passive**
>
> でも僕の写真でもあったのに。  
>  But those were also my pictures. (lit. There were also pictures of mine
> there)
>
> _raising a passive complaint_
>
> **Aggressive**
>
> どうして捨てたんだよ？！ 僕の写真でもあったぞ！  
>  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.
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If you just mean the part "what is your problem" part of the photo disposal
part, I guess: (assuming the person is acting delibaretly knowing the you
don't want the photos to be destroyed, and he/she therefore doing it)
何（を）やってるの？ or (simply to state your "disapproval"): いいかげにしろ！
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> What's your problem? - used for asking someone in a threatening way why they
> are behaving in a way that you do not like or approve of.

I think you can say...

> 何か気に[入]{い}らないことでも あるの/あるわけ/あるのか？  
>  何が 気に入らないの/気に入らないんだよ？  
>  何か文句でも あるの/あるわけ/あるのか？  
>  （いったい）なんなの / なんなんだよ！？  
>  どういうつもり / なんのつもり（だよ）！？  
>  何考えてんの / 何考えてんだよ！？  
>  頭おかしいんじゃない の/のか！？

etc... depending on the context.

> I have thrown away all the old photographs. - What's your problem? Those
> were my photos too!

How about...

> 「古い写真全部捨てといたし。」  
>  --「はぁ！？どういうつもり（だよ）！？自分だけのもんじゃ ないでしょ/ねーだろ！」
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