@oamadrigal, you answered one of my questions but not the other. I am curious how you cleaned out the AC compartment without taking the ductwork apart.
My other question was about the route you take. Have you driven in a different environment to see if you get sick? For example, if you currently drive through a city, then try a drive in the country or visa versa.
Allergies are about tipping points. For example, if you drive in the city where pollution is generally higher, and this car adds only a tiny bit more to the air inside the vehicle, that could be the tipping point for your allergies. A drive in the country may not reach the tipping point, just as driving a new car doesn't.
If you drive mostly in rural areas, a nearby farm using a certain chemical could be the problem, but that should also be a problem in your new car.
Last new question, just how much do you plan on spending to find the source? All new seals in the engine and transmission will not be cheap. If you haven't done the second timing belt change yet and want to keep the car, you can have all the front seals changed for only a few bucks more than the belt change itself and that could be worth doing. Rear mains seldom go bad but a new oil pan gasket might be justified, but that will cost even if done concurrently with the belt job.
A new cat and new exhaust system is pretty expensive. At this point, after 15 years of good service, I'd just let the car go and not spend a lot of money on it, but maybe you are just more curious than I am.