For us, back in the days when we had allergies, we used regular pillowcases and sheets but covered the mattress and pillows with impermeable covers. The regular sheets/pillowcases can be washed regularly in a fragrance-free detergent (the mildest and most natural you can find), and the lined covers keep the dust mites as well as the pillow/mattress fibers away from the person. Just be sure you don't get really crinkly ones, as they're noisy every time the person rolls over.
As much as it's nice to air dry sheets in the sun, I wouldn't do that in the pollen season unless/until you know for sure what she's reacting to.
I agree that changing the allergy meds around can make a difference, both by the time of year and also by the individual sufferer. You can talk to the doctor, but don't forget your senior pharmacist is an incredible asset. I've gotten rid of all my allergies and my husband is just about done with his (no shots or meds needed), so I'm not as up to date on the medications as I used to be, but I see my local pharmacists as extremely knowledgeable.
I'm not sure what "nasal wash salts" are but perhaps that's related to the Neti pot, which uses water, salt and sometimes a pinch of baking powder. Those worked for us but I think they are hard to use with a young child. There's also a right way and a wrong way to do it for both effectiveness and preventing infection. They are good at sweeping out the pollutants and the excess mucus though!