To reduce breathing irritations while you are dusting , use a slightly damp cloth. For wood and chrome, dampen the cloth with lemon oil, which also adds a nice shine.
If you use a cleansing powder to scrub surfaces, wet your sponge or cleaning cloth first and then sprinkle the powder on it. This will keep the powder from hanging in the air and save you from respiratory, throat or eye irritation.
When cleaning with chemicals such as bleach or ammonia, never mix them with other cleaning agents. The result could be toxic.
I recommend that you use a mask over your nose and mouth when using bleach or ammonia based products.
Beware of "second hand dust" emitted from an old vacuum cleaner. Use a newer machine that has a microfilter bag or a primary filtering system such as HEPA. Empty the bag or canister often.
Consider replacing your throwaway HVAC filter with a permanent and more effective electrostatic filter. You can then just rinse it with water every month or so without ever having to buy another one.
Invest in a microfiber cleaning cloth or two. They really work, and they trap dirt instead of spreading it through the air.
If you suffer from dust mite allergies, try this three-fold plan for relief: use dust mite-proof mattress covers and dust mite-proof pillows, use an air purifier to reduce airborne allergens, and vacuum in the bedroom at least twice per week.
Start adding up all the fragrances and dyes in your laundry soap, dish soap, hand soap, household cleaners, toliet cleaners, toliet paper, deodorant, shampoo, etc and you will realize you have a chemical soup that can cause allergic reactions. Choose unscented products whenever possible. I can send you a sample of my non-toxic, unscented cleaner, if you like.
Use an air purifier near the air return of your central air system. The purifier will trap and reduce airborne dust and allergens and enhance the quality of your indoor air.