-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!