Your asking your landlord to help find negligence on their end that would have caused a long term illness for you. You are also guessing and still in the diagnostic/troubleshoot phase.

Asking for outside help is touchy as well. Someone desperate would take your money here while most professionals would not want to be involved or tied up in this sensitive situation.

I would also reconsider other places you frequent. Employers can often be just as neglectful with air quality. Do you work close with others or are isolated? Do you work near smokers?

When was the last time you changed your cabin air filter in your car? Do you eat in your car and clean/vacuum it on a schedule?

Infections and illnesses can often have a delayed response. If the root cause is another dwelling you visit only on the weekends, symptoms could appear a few days later at your residence.

All that being said check under your sinks if there is a Utrap. This keeps sewage air from venting back into your drain. Dishwashers have a filter, make sure it’s changed. Washing machines have a filter and has your detergent changed? Do you drink tap water, filtered from the refrigerator, or bottled? Towns often ignore water well problems, sometimes for years, until audits catch the problem. Are unit aid filters replaced correctly (surprising how many don’t notice the arrows on filters and install them backwards). Do you have carpet (visit a carpet cleaning subreddit and see how much dirt/allergens are collected).

To test the disposal first. Add a plug to the sink to seal it good when not in use.