A dungeon master should be prepared for questions, and if the player is annoying them, tell them that they need to adjust their behaviour.
Yes, a Dungeon Master is not a babysitter at all, but is a human being that should set their boundaries with all people they meet.
If you don't, stuff like this will happen.
If you are unsure whether you're annoying your Dungeon Master, ask if you are and don't be offended by the answer.
Be adults about the situation, it helps for a better game.