When one is walking, one usually swings the arms back and forth. This movement should stimulate circulation in the hands. If, however, the hand turns purple, that means that blood is accumulating in the hands and the blood is not circulating upwards or back into the blood stream. That also means that there is blockage of the recirculation or there are burst capillaries in the hand and there is internal hemorrhage in the hand.
Go see a doctor and take an X-ray of the hand to see if there is internal hemorrhage or burst capillaries.