Out of context I read "My black skin itches" like "I am composed of many panels of Crayola-colored magic marker skin, and at the moment, only the black panels itch. The Razzmatazz patches, on the other hand, are fine." I'd go with the above comment: it's bad writing all around. I've seen it more with eye color, though -- when the author is so taken with whatever shade they picked out and umpteen cheesy metaphors to go with it that they mention it where it has no relevance.

It'd be less jarring if there was some context or comparison to give a significance to the observation, so it didn't read like [insert mundane physical quality] itself was the strange and noteworthy thing.