Stop the blood with compression,bandage the wound after cleaning it. You did not say how bad the blood was coming out. Apply ice for 15 minutes on and 30 min off. Try to calm yourself down and if you have to seek emergency service.
Ice (but not directly on your hand...put ice in a plastic bag, then wrap bag in a dishcloth), elevation. Take an anti-inflammatory (Aspirin, ibuprofen). If the swelling hasn't gone down tomorrow, seek medical attention.