2005 Lincoln Town Car odor in car makes me sick

I am not a pro mechanic Just my 2 cents worth.
"Shooting from the hip"
(HVAC) If I understand correctly this occurs using heat OR AC? (Both)?
Is there an odor with heat and or AC?
If so, sweet like antifreeze or musty like mold/mildew, chemical/ oil / exhaust?
With heat, Ac and blower shut off any problem?
" Pre owned" Could this be a car from a flood?
If musty consider running the car heater and blower on max for 30+ min all windows down in your driveway on max temp (NOT WITH YOU IN THE CAR) to dry and kill off molds/mildews?
If you are getting a rash consider NOT DRIVING THE CAR UNTIL THE PROBLEM IS RESOLVED!
Keep in mind what you have described could be a serious health risk!
Park the car with all windows down for some time.
How about pet dander> cat or dog "Pre owned"
Clean/ shampoo? This can get into duct work, carpet, headliner and seats.

The smell seems to be chemical in nature. The odor was not as bad in nice weather when I was able to have the windows down. I wiped the carpets and mats down with a mild detergent solution but this did not help. The undercarrage does not have a lot of mud on it. The carpets are not wet so there are no leaks in the car. I do not feel I have an alergy towards leather. Is it possible that I have a reaction toward something the car was made with.

I would hate to give up on this car.

Thanks,

John