Well, I understand about the surgery, but not about his tongue. Could you explain a little more about his present condition? And is he a man or a dog?

"stick out" = protrude, extend beyond a surface or orifice. Things can "stick out" in all sorts of ways - sideways, up, down, or hanging. If a tongue is "sticking out", it is usually in the middle of the mouth, not the bottom. Sticking out your tongue can be a controlled movement, for example, for fun or when you don't like something. If the tongue is "hanging out", then it is limp, and comes out of the bottom of the mouth, like a tired dog. So "hanging out" is a particular way in which something "sticks out". I don't know exactly the situation you are expressing.