Anything which is shot, means damaged. When I listen to Ozzy Osbourne on my mp3 player, my ears are shot (which has actually happened! haha). My knees are shot, because I'm getting older and I don't do much exercise. To be shot, is to be hit with a bullet from a gun, but it means damaged or broken, usually beyond repair, but the informal could be temporary.

Either he's been listening to loud music, or his wife won't stop talking.

"My ears are shot."= there is something wrong with my hearing