@drsharon Preservatives, dust and scents really can affect allergies in sensitive individuals. I look for allergy friendly products for everything - cleaning, laundry, bathing, etc. My sister-in-law used to think we were "being dramatic" until she developed her own allergies.

Let's talk about your concerns individually -

Candles -
Cheaper candles are made from paraffin that can release toxic compounds including formaldehyde when burned. Paraffin is a petroleum byproduct, and these substances naturally occur in it, the chemicals are "bound" in solid form, so the toxins are released when burned. Artificial scents MAY also include formaldehyde as a preservative. All of these substances become airborne when the candle is lit.
Are "natural" candles like beeswax safer? Maybe...but these also emit VOCs (volatile organic compounds) when burned, which can also be an irritant.
The best advice - don't burn candles in an enclosed space unless you add plenty of ventilation.
One alternative - battery operated candles. We put the little "votive" ones into the top of decorative candles for atmosphere, but there are many tapers and other decorative styles available, including rechargeable ones.

Puzzles - I have long had a problem with the paper dust from new ones. We shake the bag of pieces before opening to get most of the debris to the bottom. Used puzzles, already exposed to the air and with less dust, are my go-to. You can also now look on puzzle boxes for "dust free" and "pfthalate free" or "eco-friendly" labels. I have seen them on Amazon, at Barnes & Noble and at Hobby Lobby.

Pressed cardboard & pressed wood -
Buy real wood products, buy used (all the out-gassing is finished).
Or look for low-emission pressed wood products. These won't be the cheapest products but they are available:
https://basc.pnnl.gov/resource-guides/certified-low-emission-cabinets-and-wood-products
One alternative is to leave new products in a safe space to "out gas" for a period of time, then in a well-ventilated space, and while wearing an appropriate respirator, coat all unfinished surfaces with a low-VOC varnish or other sealer - before assembling if possible.
I frame pictures a lot, and choose old wood frames or metal frames, and use acid-free mat board as the backing.

Carpeting -
The cleanest, safest alternative for keeping down allergens in NO carpet.
Hardwood floors (finished with low VOC sealers & varnishes) or safe brands of laminate flooring are easier to clean and maintain.
Or choose safe carpet - here is one guide on how to find it:
https://www.mychemicalfreehouse.net/2021/05/the-healthiest-non-toxic-carpet-brands.html
Fragrances - There are non-toxic fragrances available for home use and in perfumes, but the better option is to go as scent-free as possible.
Why? Even if you find a scent that is safe and pleasing to you, it doesn't mean others will not react. In our community, the common hall is a "scent-free zone" - for men and women alike. We privately and gently explain why to anyone who arrives "bathed" in cologne.

These sensitivities are nothing to mess with, as increased exposure usually makes things worse.
What other precautions do you take?