2) An injury that is healing slowly.
3) Upset about an incident that took place some time ago.
2) That sore on your leg is still there, eh?
3) Lonnie's pretty sore about the fact that Mitch broke his bike.
Short for "sore loser" just sounds cooler.
Kid 2: Think about all the people in the world dying right now... is it still good?
Kid 1: You're such a sore!