Gentle (((hugs))) for you, those nasal sores are no fun at all. I'm sorry that you're getting them again. You certainly went a long time w/o any, that's amazing I think.
I'm gonna go out on a limb and guess the decrease in the prednisone is causing them. However, I'm not a Doctor so don't hold me to that. I do know that whenever, I try to cut my prednisone back I get either ulcers in my nose or mouth. It's usually my mouth 7 times out of 10.
As far as treating the sores, I too, use Neosporin and I will also try to rinse my nose with some saline or home made salt water to help dry it up. Sometimes, the ulcer is to sore to handle the salt water, but once it can handle it I give it a try.
If at all possible, maybe you could contact your PCM, as I know you're looking for a new Rheumy, and see if you could go back to taking the 7mg daily until the ulcers clear up.
I hope that the ulcers are the only problem you encounter and hopefully, your taper will start up again soon and you'll be able to continue to decrease the amount of prednisone you're taking. Please try to get plenty of rest and take care let us know how you're doing.
DX- RA, Lupus, Fibro, LGL Leukemia, Obstructive & Central Sleep Apnea, Pulmonary Hypertension, Bells Palsy, Gastroparsis, Blood Clots, Glaucoma, Chronic Pericarditis & Pleurisy, Severe Anemia. Way to many medications to list.