You say that this fabric was a "private" sale and not from a store. Could it be that the fabric came from someone who either had pets (dander is basically invisible and that is the stuff on pets that cause allergies) or someone smoked around the fabrics. Just a thought. Wash the fabric as soon as you can. The small pieces can be put in a mesh bag or pillow case and either hand washed or put into your machine on gentle. You shouldn't get too much fraying this way.
I get cracks in my thumbs (by the nail corners) when I handle a lot of fabric. I think this is because of the sizing/dyes. Sometimes I will wheeze when in fabric stores or even clothes stores. I've always attributed this to the dyes and I make sure I carry my inhaler.
Hope you are feeling better! Here in the northeast we've had a winter to beat all winters (extreme cold and tons of snow). Now we have rain and mud. Lots of molding leaves in addition to budding plants = lots of allergies up here. Sometimes I hate spring...