Madamekelly: so sorry to hear about your awful reaction to your fabrics! I don't prewash my fabric and find that when I have been sewing for a while, my thumb skin splits on either side of the nail. I wonder after reading your post if this is caused from the chemicals in the fabric???
As to washing your stash, I would try the basting/sewing the cut edges to cut down on the fraying. Really small pieces I would use a mesh bag for.
Good luck! Wish I lived closer, I'd come over and help you wash the stash! Hope you feel better and washing the fabric helps clear up your hands.
Anita