The cop could very well have gotten injured during events in
existing witness statements, from the car door bouncing back or in the process of trying to pull Brown into his car.
I don't doubt that he got an owie, but yeah, if he'd gotten it from Brown, there would be some indication of that on Brown's body and in the eyewitness accounts. He probably just banged his head on his car door or something and got mad like you do when you bang your head on something, with the big difference being that he is a cop and he reacted by riddling a teenager with bullets instead of just swearing at the door itself like a normal person.