My asthma is so bad my doctor has ordered me not to try to clean. A couple of years ago I did buy some allergy free cleaning products on line that worked well. I am sorry, but I can't remember the name of the product line. I couldn't afford the cleaning products and my cleaning lady.
She uses Murphy's Oil Soap on my floors. I have all hardwood and tile. She closes the bathroom doors while she is cleaning them and has the exhaust fan on and this helps.
I am sure if you do a search for allergy free cleaning products, you could come up with something.