Hello there, I talked here about the 9th Century medical textbook known as Bald's Leechbook. The Leechbook - Doctor's book in Old English - includes instruction on how to clean and dress wounds, treat infections and gangrene, set broken bones, help with fevers and even how and where to properly carry out amputations. While they were still dangerous and potentially life-threatening, therefore, there was clearly an expectation that the types of wounds like those suffered by the characters in ASoIaF could be treated, and indeed would maybe even be expected to be survived given prompt care and attention.

Not to take away from your question, but you may also be interested in the answer from /u/Trinity- about treatment of infections in the question about the scenario Suppose I live in 1116 and I cut my hand and get an infection.