The Caduceus (two snakes wound around a staff) Christmas tree baseball shirt was NOT the symbol of medicine. The Caduceus is the staff of Hermes, the Greek messenger god and also god of many other things. The wings on his staff help him to fly and deliver messages.
The symbol of medicine was the Rod of Asclepius Christmas tree baseball shirt (staff with single snake wound around). Asclepius was the Greek God of Healing and Medicine. The usage of Caduceus as a Medical symbol was started by mistake by the US Medical Corps in 1902 and this became popular.