in order from the wrist: Scaphoid, trapezium, 5th metacarpal. A 'Boxers break' traditionaly is referred to (in Britain at least) as when the impact is transferred (via poor technique ie. punching wrong) into the scaphoid causing it damage. the 3 bones listed are small and close together, and injury to one, will cause referred pain to the others, as well as inflamation of all the connective tissue and musculature, of which there is a huge amount to allow for all the fine motor skills possible in the hand.
My advice stands regardless of what bone is injured. Bones have a fantastic blood supply and heal far quicker than tendon and ligament.
Learn to punch properly for the future, and you will minimise the chance of this happening. One hand can be excused, but both is just careless.