I use the pine pellets similar to woody pet but just not that brand name but I don't activate with water and I use the deep litter method. So it's a nice dry firm pellet base. They eventually get more broken down with the moisture in the poo and with the stirring up, and it is also very humid here, so it is a pretty dust free product when used this way. The birds themselves produce a lot of dander dust. I don't want to say wet anything down because mold allergy could be causing you a problem as well.
I use DE fairly liberally so that does provide some dust but you could eliminate that and see if that helps your situation. Also, a dust mask may help. You can't be allergic to your chickies!!!
But honestly, sand is probably the way to go for you.
Orchidchick