Great questions! Post aspergillosis lungs can be very sensitive.
Your car has an air filter for the ventilation system. In most it is on the air intake behind the glove compartment. Until I started paying attention, I didn't even know it existed, but now my husband changes it twice a year & we always keep the windows up. Also, it may be that there is mold in your AC ducts or carpet/padding? I had that once in a car that had been abused before I got it. I bet you can find out on line how to deal with it.

As for the HVAC - we put in the best HEPA filtration system we could when we got our new furnace 5 years ago, but skipped the UV because the reviews on how effective it is are spotty. We run our house fan on low & change the filters more often than recommended. The best one for you will depend on your system and how you use it.

A very big thing we did many years ago was to remove the "hiding places" for dust, mold spores, etc - all carpet except the guest room & stairs replaced with hard flooring. The carpet that is there is very low pile. All curtains are completely washable, or were replaced by easily cleaned shades/blinds and wipeable valances.

In addition, we run smaller HEPA filters in our living area - one in the main area & another in our bedroom, as well as one in my much used studio/sewing room. (Also in our very tiny Texas house.) We find this helpful as we both have bad allergies. I chose Honeywell ones because the filters are widely available, easy to change, and the machines tell me when the filters need changing.

All of these combined make life more comfortable. Sue