I see from where you live, that having numerous Vets to chose from probably is not an option. If it were, I would say to change Vets, but I realize that might not be an option.
I think your Vet is over-using steroids. They have so many side effect, that any other anti-inflammatory / anti-allergenic drug would be a better choice. Bute and antihistamine drugs have far fewer side effects and do not weaken the immune system. I think a diuretic would also be helpful if she shows edema and/or fluid in her lungs again. Long-term use of diuretics can be difficult to hard to wean a horse off of. If steroids MUST be used, I think they should be accompanied by a broad spectrum antibiotic (at least that is what my Vet thinks.)
I think a blood chemistry panel and a CBC should have been done in the beginning. It surely should be done now. The white cell differential will indicate allergies and/or parasite problems as well as any infection. The blood chemistry will indicate liver and kidney problems as well as many other things that can be wrong. Without having these blood values to guide him, your Vet is just shooting in the dark. It is like pointing out the door at night with a shotgun and hoping you hit the target when you can't even see it.
I would also deworm this horse with a Power Pak. I have seen parasites cause this drastic kind of reaction in a horse before.