There is a word for this, especially in equine medicine. It is called galling.
Per Saunders Comprehensive Veterinary Dictionary, 2nd Edition (p. 483), a general definition of a gall is:
a sore caused by chafing; said commonly of horses
There are a couple of other related definitions in the same dictionary:
girth gall (p. 499): a skin abrasion on the chest just behind the elbow of a horse caused by pressure or movement of the girth while being ridden. Caused by sharp edges of the girth, girth adjusted too tightly or too loosely or a poor conformation of the horse.
saddle sore, saddle gall (p. 1005): a pressure sore caused by bad riding technique or more commonly a badly fitting or poorly stuffed saddle.
As for in human medicine, Dorland's Illustrated Medical Dictionary, 28th Edition, has one definition of gall as follows (p. 673):
a localized swelling or skin sore caused by friction.
As for the verb form of the word, gall is both a transitive and intransitive verb (see this entry on FreeDictionary.com)
to make sore by rubbing; chafe severely: The saddle galled the horse's back.
to be or become chafed.
Here are a couple of examples of gall being used in a sentence from the Wordnik entry for galled:
His flesh was galled by many days of contact with the haul-rope.
His shoulders and chest, galled by the pack-straps, made him think, and for the first time with understanding, of the horses he had seen on city streets.