I know what you are going through! Never a smoker, I've been diagnosed with Emphysema and the doctor told me to stay away frm cutting fabric - expecially cotton! How do you that as a quilter? You learn to wear an N95 mask when you cut it. If you are not allergic to latex, perhaps you could wear latex gloves when handling the fabric prior to washing.
I also wash my fabric, dry and remove from the dryer when it beeps. Fold, then iron when ready to cut! Since I still have a closet rod in my fabric closet, I put a lot of the pieces on hangers that trousers were returned from the cleaners on, then hany them up. Hope this helps some. Hang in there!