Almost 100% of the time the problem is mold and other microbial growth in the AC, AC closet, or ducting (AC system).

There is always moisture in the AC system from air blowing over wet AC coils and this moisture along with accumulated dust and dirt in the ducting is enough for molds, duct mites (that eat mold), and other irritants to thrive. The AC spreads these irritants throughout the home whenever the AC is running. This particularly impacts the young, immune compromised, and the elderly.

Keep in mind, all AC systems (AC + ducting), except when brand new, have some level of mold contamination. All household dust contains mold, dust mites and other irritants.  Regular duct cleaning is extremely limited and does not eliminate mold and microbial growth from throughout the ducts.  And does not solve the commonly occurring problems that cause heavy microbial contamination.

In Florida, duct cleaning is not a licensed industry. In a best case scenario the regular duct cleaning will eliminate some loose dust; but worst case they damage the ducting and/or spray illegal biocides into the ducts which can be hazardous to your health. They do not in any way, shape, or form eliminate the mold growth in ducting.