Really dull rounds. They always have a little spark of bounce or brightness that flats never have, and they never have the thump you get with flats.
My guess is that the process of grinding down the round winding creates microscopic burrs, which get flattened out after some use. My fingertips feel like they've been "lightly sanded" after playing a new set. To be clear, this is a lot less aggressive than the effects of rounds, but nothing like the silky smoothness of flats. The callouses I get from half rounds are much closer the the ones I get from flats.
Ouch! Obviously they're a no-go for you, then. I am not very hairy, but I don't think my arms ever come in contact with my strings... Do you have a wild playing technique or is this happening in passing?