Yes, you should be concerned. Household dust may contain allergens (e.g. pollen, mold, animal dander, insect parts, and some chemicals), which can trigger or exacerbate an asthmatic attack.
Controlling dust requires daily housecleaning and regular laundering of bedding. To keep dust from becoming airborne, cleaning using damp cleaning methods instead of sweeping, and vacuuming using a high efficiency particulate air (HEPA) vacuum is recommended.
