Yes, this is very possible. Dirty central air systems in houses/buildings can cause all sorts of trouble for people with allergies, and a free-standing fan that's covered with dust is no exception to this. You might try cleaning the fans and see if you notice any improvement. Good luck!
Chronic Lyme Disease, Gluten & Sulfite Sensitivity, Many Food/Inhalant/Medication Allergies & Intolerances, Asthma, Gut issues (dysmotility, non-specific inflammation), UCTD ("Secondary Lupus-Like Syndrome"), Osteoporosis, Anemia, Lymphopenia, intermittant Pancytopenia, chronic malabsorption/malnutrition, etc.; Currently TPN-dependent.
Meds: Zofran, Pulmicort, Vitamin B12 Shots, Heparin (to flush PICC line).