The correct symbol of medicine is the rod of Asclepius.

It is a single staff with ONE serpent wrapped around it. It’s an ancient symbol that is associated with the Greek god Asclepius, with astrology, with MEDICINE and HEALING. In ancient Greek mythology, Apollo’s son Asclepius is the god of medicine and healing. And apparently, Hippocrates was a worshiper of Asclepius.
The WRONG symbol of medicine that a lot of people tend to mistakenly use is this one:

This above image is the caduceus, which is the symbol of Hermes, another Greek god. It has meanings of “commerce, eloquence, trickery, and negotiation” (thanks, Wikipedia). It may have come into use for a medical symbol when Hermes started getting linked with alchemy. And then people started mixing it up with the rod of Asclepius when things were documented wrong, and all kinds of people became confused about it.
But if you didn’t know about this before, now you know. One staff. One serpent. Sure, it’s just a little symbol, but we have to represent our profession correctly, y’all.
(sources and stuff like that)