I would suggest clarifying the question. Different societies had different norms and regulations on the medical profession, as well as other healthcare-related trades and agents. The same goes for how these norms developed over time. Maybe it would be better if you narrowed the question down to a given timeframe and place so it could be answered with more accuracy.

Very briefly, medical education is ancient -- medical education existed in Egypt, Babylon (this article was recently published about a medical student named Kishir-Ashur), and of course Greece, where the Hippocratic school was dominant. We know there were formal medical schools in Rome, and most notably in Alexandria. The beginnings of modern medical education in the West began in Italy; Salerno makes the claim for the first "medical school" as we currently know it (side note: they have a fascinating "virtual museum" if you visit; I dragged my wife there and pestered the poor docents on a trip during residency). Their curriculum would have consisted of Latin translations of Greek texts (all via the Arab world, where medical education had been flourishing for several hundred years).

Your question might be getting towards the professionalization of surgeons, which happened MUCH later. Surgery was considered a trade in the West, performed by barbers, and did not get formally adopted into medical education until really the 18th century (though I'd really date Pare as the first "academic" surgeon, which is in the 16th century).

I'll back u/BormaGatto here on the vague question, but re: "degrees", the standardization of medical education wouldn't happen until the late 19th and early 20th century (first in Germany, and then in the US with the Flexner report). Many degrees offered before this period would have been of drastically varying quality.

Hope that helps!