Medieval medicine and the time period it kept someone alive in the Latin West could frequently be described as "nasty, brutish, and short," indeed. (It's not just modern bias, either. During the Crusades, Muslim doctors and chroniclers in the Near East observed Frankish medical practice on and off the battlefield with horror.) And a lot of anecdotes about people who died in falls off buildings, from late medieval English coroners' reports, recount that they died immediately--no chance for even nasty and brutish medicine to get involved.

Nevertheless, there are indeed some examples of people who survived falls off walls, buildings, horses. A French man who fell off a ladder in 1403 experienced a traumatic head injury that left him severely cognitively impaired, with extreme memory loss and a tendency towards impulsivity and anger (we know about this story because he later went after his wife with a pitchfork). In 1282, the king of Serbia fell off his horse so badly that he could never again walk properly, and was more or less forced to give up the throne. An early medieval abbot is described as having "at once lost all power of feeling and movement" after a similar horse-related accident, although he eventually recovered the ability to walk.

Workers like carpenters and masons who were injuried in worksite falls, and thus found themselves unable to work, would be counted among the "deserving poor." Thus, hospital (hospice/homeless shelter) records from the later Middle Ages sometimes indicate that a particular resident had been injured in a fall, although specifics for the type of injury are not always given.

One place we hear about major falls that caused massive traumatic injuries (including paralysis/"useless limbs") is, of course, miracle stories of healing. There are some cases, like where a monk who fell and shattered basically every bone in his lower body was swiftly taken care of by doctors who set the fractures (apparently properly), but also by the local saintly bishop who prayed unceasingly over him, where medical treatment was both a factor and immediate. But other cases I mention here because of the IAF/GOT angle. The character in question spends a good chunk of the series being carried around on another character's back in a sort of basket. Well, Martin apparently did his research. Because in addition to people who could drag themselves around with crutches and mentions of litters carried by multiple friends, we have both written records and manuscript illuminations of people--mostly children--being transported in baskets to shrines for attempted healing.