Also, consider feeding her wet - both her hay and what ever feed you have her on. If you can feed her outside instead of in a stall - that may help and if indoors - regularly "wet down" the stall - ceiling, walls, bedding - to lower any and all dust. During the summer/fall when it's not really humid (yep, that does occur, LOL), we often hosed stalls down several times a day at the boarding barn with the vets office. Some more heavily than others - due to the residents' stall habits - pawing and stall walking throw lots of dust into the air where it stays and then adheres to everything until it's "blown" back into the air by a fan, breeze, cough or snorts or even a kick to a wall...
For our mare (large pony, part arab), after moving down from MT and bred & originally from N Dakota, this helped immensely. Other wise, she was able to be maintained on "Anihist" powder added to her feed during the summer and fall when she had her flares with heaves. When I sold her, the new owners maintained her the same way - though when she went to a trainers barn for a riding tuneup she got pretty bad for a while (the barn was horribly dusty - several horses dug holes constantly in their stalls and I would wear a bandana over my face when I was in that section of the barn). Moving her from the barn to an outdoor paddock fixed most of the problem.
Another large pony sized, purebred arab mare that we owned, developed a cough after a bad choke incident which took HOURS to clear. The cough would show up like clockwork about the same time every year - mid - fall - starting the year after the choke incident. We often used liquid Breathe EZ - first purchased from the vet, then later thru vet catalogs w/o a prescription. I also used it on the "heavey" mare - as it seemed to help. We would just syringe it into their mouths - they both learned to like it.
I also use it to this day for a cough if I have some on hand when needed. 1 drop placed on your finger, placed on the back of your tongue, opens up your nasal passages and stops coughs for hours~! Works wonders when OTC cough remedies quit working, especially if the cough is due to sinus drainage due to seasonal allergies. I believe the main ingredient is Eucalyptus but can't remember the rest at the moment and haven't looked it up in a long time.