I just wanted to weigh in and thank you for being concerned, Lizzie.
I heartily second David's advice. I suffer from allergies and asthma and am currently planning a 3 week trip to Europe covering 5 countries. It has required literally months of searching and corresponding to find rooms that will not make me sick. I have encountered all manner of issues, from outright misrepresentation to incomprehension regarding what it means to provide and "allergy-free" or "hypoallergenic" room (e.g., small hotels all over Switzerland report providing these types of rooms but almost none know what this means--they use perfumed detergents and cleaning supplies and air fresheners).
As long as you room is truly clean (no dust, mold, mildew, damp smell) and entirely smoke-free, creating an allergy-friendly room is very simple. Just eliminate all added scents (air fresheners are deadly to the lungs of any human being--not an opinion but a chemical fact of life when concentrated tiny particles, like perfumes, are added to the air we breathe). As David said, clean with unscented products (large hotel chains will wash down the room with vinegar and baking soda, then rinse and dry with microfiber cloths). Choose disinfecting agents that do not have added perfume and use them only in the bathroom -- sparingly and with the vent fan running. Choose "Free and Clear" laundry products --no perfumes or dyes. These are inexpensive and readily available.
In between washings, throw all fabric, like duvets and pillows, in a hot dryer for 20-30 minutes. This eliminates most dust mites and bacteria. Never use carpeting (previously finished wood, linoleum, tile, concrete--all are OK). Use washable blinds rather than drapes. Eliminate unnecessary upholstry. Never remodel or renovate with products that contain volatile organic compounds. Keep your air conditioning scrupulously clean and free of mold. A well-maintained air cleaner is a plus.
Lastly, be absolutely honest about what you do or do not provide. A guest's health will depend upon it.
So the trick is mostly to eliminate things, not buy expensive extras. You will find that all your guests will love breathing fresh, clean air.
Again, thank you for being interested and concerned!!
Linda