How does one become allergic to dust?

Allergies are common: Technically, people are not allergic to dust, but instead are allergic to dust mites. These are tiny insectlike critters that are not visible without a microscope that live in carpets, pillows, mattresses, comforters etc. Plain pure dust certainly can be an irritant causing sneezing and itching. But the immune reaction of allergies are reserved to the mites themselves.

Dust mite contact: Dust mites live in bedding, carpeting & upholstered furniture but not in vinyl-covered crib mattresses. Enzymes in their fecal pellets trigger an immune response when they contact the skin or when they are inhaled into the lungs. These same enzymes may digest the seal between skin & airway cells permitting them to penetrate deeply where processing by the immune system elicits an allergic reaction.