Do we have the same bodily functions as animals that switch off pain after a certain amount of injury?

The body creates many different forms of adrenalin when you're stressed and one of which can cut off pain for a short amount of time. It normally only happens when part(s) of your body is badly injured and it gives you a short term stress reaction boost to give your body enough time to get to a safe spot before the supply of adrenalin runs out.