You are in Member Communities . The first two allergens that come to my mind when you mentioned coughing around cardboard are molds and roaches. Mold spores are released when the cardboard is handled. If so, keeping the cardboard dry would help.
Cockroaches also love living around old stacks of cardboard.
Many people with asthma are allergic to cockroach droppings, which turn into dust that is easily inhaled when the area is disturbed. A HEPA room air filter will remove these allergens from a room, but if your face is near the source, the room air filter won't help. A tight-fitting mask would reduce your exposure, but before I'd put up with wearing a mask, I'd go to an allergist to get skin tested for the common aeroallergens that are associated with asthma. House dust mites love fabric, but not cardboard, since their only food is skin flakes from humans or animals. All rights reserved.