Cooper doesn't get a chance to drink in any of her blood before her elbow smashes him right in the nose. He pulls away with blood streaming out. Cooper takes a step back, brings the gun up, and pulls the trigger. It produces nothing, as all the bullets have been expended.

His left hand comes up wipe some of the blood away from his nose. He hasn't thrown the gun away. Sure, it's out of bullets, but it's still a nice blunt object he can use to whack Alex over the head with. Cooper doesn't really have a fighting style besides trying to do enough damage to the other person so that they don't get back up. He charges towards Alex once again, his stubbornness outweighing any common sense he has.