Keep in mind, I do not claim any expertise in this. However my bits and pieces I have collected I understand a few things.
Medical roman stuff... well it was rather simple for the most part, I will spare you some of the pointless details. Essentially they thought there were 4 biles or humors that kept the body going and in balance. They thought color was everything. If you were low on yellow bile, you needed to eat or ingest yellow things, and so on. It wasn't always that simple, they would make recipes (some of them very complex and reasonably effective at lessening the suffering. It was not very potent like today's medicines, mostly it was just to take the edge off.) The Romans had access to a particular drug that made their doctors feared and believed to have supernatural abilities... they could give life and death. This actually came about through the use of European Mandrake which is a natural anesthetic. (It scared the crap out of the Celts.)
Generally their entire concept was to remove as much of the problem in order to allow the body to heal itself. They figured out some very minor surgeries (mostly on war wounds to remove shattered bone chips.) However, more common was the use of "searching the wound" in which they would examine it closely and remove any left overs. Again, the intent of these doctors was not to repair the damage because they simply didn't have the ability to do that, but to ease the suffering. THAT in and of itself will let you understand old medicine and the logic behind it. A doctor was not just some guy that patched you up, he was also a companion and a trusted confidant. "The Eagle" seemed reasonably accurate (from what I can tell) in the roman medical treatment with the exception of the "bite on this wooden stick to not break your teeth from the pain." They probably would have just drugged him with mandrake.