People with allergies fare better when dust and grime are kept to a minimum. Try not to use aerosol sprays or products containing harsh chemicals or odors that may irritate your airways. But your home will need more than a dusting with a dry cloth, which just propels allergens into the air. Instead, wipe down hard surfaces and floors with a slightly damp cloth. In humid areas, use a bleach solution.
Bleach kills mold, and, unlike some other exotic (and potentially dangerous) chemicals, you can get it at the grocery store. Wipe down surfaces in your bathroom as needed. The label on Clorox bleach suggests that you clean floors, vinyl, tile, and your kitchen sink with a solution of 3/4 cup of Clorox bleach per gallon of water. Let it stand for 5 minutes and then rinse. Use a regular fungicide for tough locations, like the basement. Of course, don't use it on fabrics, or they'll get bleached.
If you're allergic to house dust, pet dander, or another common household allergen, get someone else to take care of cleaning that carpet, such as a teenager or a professional cleaning service. The cost of hiring a helper is a small price to pay to avoid an allergic reaction.