Ramsay has made several "adjustments" to Theon during his imprisonment and torture. These include removing fingers, toes, and a certain "other thing." He's likely to have done a bit of flaying to poor Reek as well.

But, what prevented Theon from bleeding out in the dungeons of the Dreadfort? Without some medical attention, someone to cauterize severed fingers or toes or prevent infection, Reek would have probably died a long time ago.

GRRM's world is clearly one where such infections exists. Kahl Drogo seemingly dies of an infection, although it may have been that Mirri Maz Duur's poultice was tampered with from that start. The point being is that Ramsay surely would not be able to have reek to toy with if he succumbed to gangrene. Someone would have to treat him.

But Reek makes it seem as if he has not received any medical attention. He is very unwilling to be examined by Roose or others, fearful that Ramsay would punish him for disobedience. In the following passage it is implied that Reek has unattended wounds that have not been seen by persons other than Ramsay:

“A bath?” Reek felt a clenching in his guts. “I … I would sooner not, m’lord. Please. I have … wounds, I … and these clothes, Lord Ramsay gave them to me, he … he said that I was never to take them off, save at his command …”

I do not believe that there is textual evidence of a maester residing in the Dreadfort, but certainly the Boltons must have one. Every noble house of high enough standing is assigned one by the citadel. And if they do have a resident learned man, where is he? Does he tidy up the messes made by Ramsay and his Bastard boys? Or is it Ramsay himself who is patching reek up today so he can flay him again tomorrow?