I don't know what a head splinter is, other than the obvious, but UD should never have approved the previous definition. Everyone knows that a song stuck in one's head is called an ear worm.
Dude 1: Man, I got a head splinter!
Dude 2: Do you want me to get my tweezers?
Dude 1: No, it's a song.
Dude 2: Don't be an idiot, that's called an ear worm!