I am talking about using techniques for dealing with choking, cleaning and wrapping cuts and burns, using the recovery position for unconsciousness, and using CPR in those rare cases where it is used to restart someones breathing (as opposed to just keeping them alive until the professionals arrive.) Please interpret the question how you like in terms of other first aid techniques I may have missed, I am aware that the middle ages/ medieval period spans a large amount of time and cultures, but please just choose the aspects of it that you can give a cool answer for.
In Medieval England such a person would be known as a Cunning Man or Woman. Their modern knowledge would be good but by no means exceptional. Good bone-setters were not unusual in the Middle Ages, as we know from excavating graveyards and finding skeletons showing evidence of having some serious injuries treated successfully. So a modern first-aider would not necessarily be seen as someone with magical powers. And a modern first-aider would be hindered by lack of modern materials we take for granted - sterile dressings for example. Incidentally in the unlikely event of being thought to be in possession of magical powers, there would be no danger of being accused of being a witch. Plenty of Cunning Men and Women used spells as well as other more useful techniques.
EDIT: I've quite rightly been asked for a source. My principal one is Keith Thomas' Religion And The Decline of Magic