I think it's the fact that, if your mind thinks you are in pain, you're gonna feel pain. Not always though. I've had non lucid dreams where I shot myself in the head and I could feel the bullet go through my skull, and yet it wasnt really pain... But then I've had dreams where smaller injuries really did hurt. I think maybe that's because I was in pain in real life? Maybe not as bad but like someone said, if you focus on it your mind makes it seem extra painful.

I wanted to add that, sometimes people that are missing an arm can feel pain in that arm. Clearly they don't have an arm that could be in pain. It's your brain's interpretation of pain. Signals beign sent in the mind. Same could be true with dreaming.