People like to think that Medicine and Science happen in Sterilized rooms, where everyone wears a lab coat, and everyone knows exactly what the outcome of everything will be. That is not science, it might be a routine test some scientists are doing, but that is not the bulk of how science moves forward in leaps and bounds.
For example, Penicillin was not discovered by someone working for Pfizer in a sterile lab, trying to cure disease. It was discovered by a messy scientist, who was eating in his lab space, and accidentally left a sandwich out. When he came back to the sandwich days later, it had mold growing on it. He put this mold in a Petri dish with other Bacteria, and it ate all the other bacteria. This is how Antibiotics jumped forward.
The first person to invent Vaccines also kind of did so on accident, or at least the guy he copied did. The inventor of Vaccines is Edward Jenner, but 30 years before he invented Vaccines, his friend John Fewster was randomly doing studies where he gave people smallpox on purpose so he could study their reaction, and one time he did it someone didn't react and he questioned them, and it turned out that that person had previously had Cow Pox. So he told people about this and 30 years later Vaccines existed.
Not all science happens like this, but a lot of it does. A more modern example is a spider they found in the Amazon, this spider ha venom that works similar to Viagra. But when it bites you, a guys penis will get so hard it explodes or stops working via ruptured blood vessels or something. So now that some people have died from this (I think you would die, or hope kinda) they are now working on a way to turn this venom in to the new Viagra. So this kind of stuff happens all the time.
I just wanted to point those things out to say, Western Medicine is not the regimented, sterilized, perfect art we think it is. It is just regular people that went through some higher education, and now they are figuring some stuff out. And I told you that because I want to show you where it comes from.
Western Medicine starts in ancient Greece with the worship of the God Asclepius. Asclepius was always identified with snakes, and usually a non-Venomous snake would be kept at his temples, the snakes had free reign inside the temples and were allowed to slither on the floor in rooms where patients slept. The Aesculapian snake is actually a species of snake.
The Temples were known as Asclepeion, and they operated much like Hospitals where people would come from all around to come be healed. The way the Doctors would heal the person is by inducing a dream and interpreting it, then giving the person a prescription based on the dream. This is almost identical to Native American Shamanism, you may have heard people call Ayahuasca "Medicine", this is the context of that. The Shamans are meant to take Ayahuasca and come back to this "realm" with a prescription. And according to legend, the plants themselves actually told the Natives how to make Ayahuasca, since you have to mix 2 specific plants in the jungle. If you want to try to find the ancient Greek writings about this, there is supposedly a book called "Sacred Stories" by Aelius Aristides. He was one of these doctors.
The Rod of Asclepius is a common medical symbol, it is a staff with a snake on it. The doctors themselves were known as Asclepiad, the most famous of which is probably Hippocrates. Hippocrates invented the Hippocratic oath, which Doctors still say today.
Hippocrates is still considered the Father of Western Medicine to this day, he identified a few things that are still named after him sometimes, like Hippocratic Fingers, and Hippocratic Face. He also started the classifications like: Acute, Epidemic and Chronic. He also invented the Hippocratic bench, which was a forerunner to Chiropractor tables and some Torture Devices.
I am not suggesting we go back to the Greek Medical model, I just wanted to point out that the things we take the most serious, sometimes (usually) started as people playing with snakes and interpreting dreams.