Does dust allergies cause sinusitis? can sinusitis be caused by allergy to dust?

Yes: Allergy cause inflammation which blocks the sinus cavities and may promote infection.

Yes: Sinuses have tiny openings into the nasal cavity allowing air exchange. When the nasal cavities are "congested" either from allergies (any cause), or a prolonged cold, these openings are blocked. The oxygen in the sinuses then slowly disappear and thus allows excessive growth of bacteria and consequently may cause sinus infections.