How could I numb a broken shoulder?

Broken shoulder. In an emergency find a way to place the arm across the chest with elbow bent at ninety degrees, and then wrap the arm against the chest by wrapping around the chest to accomplish immobilization of the arm at the shoulder. Then obtain medical evaluation as soon as possible.
You could try. Intermittent icing. If you are having surgery speak with your anesthesiologist about receiving a brachial plexus nerve block.