Yay! We now have a clean garage!
Ironically, one of the things that can trigger allergies when you are cleaning your house to prevent allergies is the cleaning products and tools used. I have a friend who was hospitalized for some days before the doctors finally diagnosed her problems as lung irritation being related to cleaning products. She had to undergo a number of tests before this diagnosis was made.
In general, trial and error can help you determine what bothers you and/or another family member. Cleaning products can cause respiratory allergies and possibly skin allergies, too. Try different clothing detergents and different cleaning products. Products that are more likely to be irritating will have strong fumes or odors. Products that are delivered by some type of spray also may be irritating. Products marked as hypoallergenic might be a better choice, but, again, you will have to determine whether or not it is safe for you. Green products may or may not be less caustic and less likely to trigger allergies.
Good old fashioned cleaners like baking soda, vinegar, and lemon juice are not as likely as commercial cleaners to trigger allergies, but make sure that you know how to use them.
You may need to wear a mask while cleaning. Also, use dusters that trap dust rather than just stir it into the air. Be careful how you empty your vacuum's chamber or change vacuum bags. Borax is a good old fashioned cleaner, but it can cause severe reactions, especially if you are exposed to too much borax dust.