I think we knew that kibble wouldn't work
There are two three other options, though one might have been tried, though both would require feeding the diet that she does better on. .
The first option is that this is partly a staph infection, and treat with cephalexin. Might be available over the counter as a fish antibiotic, would have to look.
The second is that this is autoimmune. In this case, the antibiotic doxycycline (available as Bird Biotic) and the supplement niacinamide (not niacin, must be niacinamide) combine to treat this, to some degree. It is used in autoimmune consditions such as pemphigus. I would combine with MSM.
The third, may be tried alone, or combined with one of those above, is the most toxic trial. If this is yeast (or if yeast is made worse when given an antibiotic), ketoconazole can help. The problem with this is that keto is more toxic to liver and kidneys, though my dog's blood values didn't have any problem on it. It can also suppress the adrenal glands. But if there is yeast...
Again, these all involve costs and may not work.
I just feel terrible that you are in this situation, I am so very sorry. ((Hugs))