You can get your ducts cleaned out if you can find an HVAC company with the proper brush/vacuum system -- they run it down one duct at a time and clear out tons of stuff. Sure, an air purifier helps too, but if you have an ongoing source of mold, you need to address it first and then worry about air. I live in a 50-year-old house and never smell mold.

Do you have rigid ductwork or flex duct? If the latter, it can’t be cleaned, let alone trested.