My son did this when he was 3 and, yes, I had to miss work to take him to the pediatrician since no amount of nose blowing would dislodge it.

A friend of mine had to leave work because she got a call from the police about a car accident in her apartment. A neighbor's drunk ex-boyfriend had driven his pickup truck through the exterior wall, through the neighbor's apartment and finally came to a stop in the middle of my friend's apartment. She had to move out that day and quickly since there obviously was some question about the building's structural integrity.