It really sounds more like you are seeing an allergy to the alfalfa or the grass. I would want to talk with the vet about this (have them out when the symptoms are present) because an anthihistamine might solve your problem.

I did horse rescue for a lot of years and we had a horse that was very similar to what you are describing. We had to put him on a diet of beet pulp, grain and grass forage (comes in a large bag at the feed store) and this was the only thing that helped.

Horses that suffer from the condition are usually allergic to mold particles in hay dust, although other allergens such as pollens, chemicals, microbes and substances found in foods, medications and the environment can also trigger the condition.

They seem to suffer more in old barns where dust and allergens are high.

My suggestion to you about the barn would be that you not stable her at all. If you do, be sure that you don't use shavings or bedding at all. I would, instead, use floor matting that will not throw up dust. Old conveyor belts work well as a cushion and they are not expensive. You can, of course, opt for the expensive rubber matting. You can get old conveyor belts from a manufacturing plant in your area.

I would also consider switching her from a diet of hay to a diet of grass forage. Talk with your vet about this before you do. Grass forage contains little dust and is cleaner and dryer than hay. It comes in a bag and you can get it at your feed store. I would keep her on pasture and feed this instead of hay when she is in the stall.

When planning your barn, be sure that you leave her space open if you do decide to stall her. Use metal grates instead of walls so that you won't restrict air flow. When you clean her stall, take her out of it so she won't breathe the dust.

Consider using lifestyle supplements that help to curb the production of histamines in the tissues. Bioflavonoids (plant-derived protective substances), including those derived from Camellia sinensis and Vitis vinifera, have been reported in numerous studies to inhibit the release of histamines. The antioxidant vitamins A, C, and E can also be helpful for horses suffering from COPD to help combat free radical damage produced during the stress response and to promote tissue repair.

source for italics

I hope that this helps. Let me know if you have more specific questions.