Dust mites feed on the organic part of house dust (often, mostly skin flakes from us!) and then excrete an allergen, a substance that causes an allergic reaction, that can stuff up our nose or even lead to life-threatening asthma. Even if you could eliminate all dust mites, which is unlikely, their allergens would remain in bedding, carpets and other fabrics where dust mites live. When these fabrics are disturbed they release allergens into the air.
One of the best ways to prevent an allergic reaction to dust mite allergen is to put a barrier between you and the allergen, especially at night. If the allergen never gets airborne, it can't end up in your nose!
Since mattresses and pillows are a prime source of dust mites and dust mite allergen one solution is to cover them in special fabric that separates you from the allergens. Until recently these fabrics were made of plastic and tended to be very uncomfortable. Newer microfiber materials are more "cotton sheet-like".
See more suggestions for dealing with house dust mites at 'Bugs.