When someone asks the same question over and over
Nagging
which means to annoy or irritate somebody with constant urging.
It is often used to indicate constant complaining, but it works here.
Synonyms include:
harass, badger, give someone a hard time, hound, harry, criticize, carp, find fault with, keep on at, grumble at, go on at;
I got mad because he was nagging/badgering/harrassing me.
Pester:
To behave in an annoying manner towards someone by doing or asking for something repeatedly.
John has been pestering her to go out with him all month. (Cambridge Dictionary)