Hello, I'm Dr. Deb and will do my best to help you today.
I'm sorry for this problem which your pup is having; I know it must be quite distressing to see her this way.
Based on the description of her symptoms, I would agree that it sounds as if she has developed puppy strangles aka juvenile cellulitis. In fact, your description couldn't be more classic for this condition which is considered autoimmune in nature and thus requires high doses of steorids (2 mg/kg twice daily) in addition to antibiotics if infection is present (which is often the case). A definitive diagnosis can be confirmed with a biopsy (prior to treatment) although the presentation is typically so classic, that most vets don't bother.
Once the lesions have significantly or completely healed (which might take a few weeks), then a very slow tapering off of steroids is done which can take up to 4-6 weeks in some patients or even slightly longer. I can't be entirely sure, of course, but I suspect that the steroid dose may be decreased too soon which is why she's having a relapse.
Other possible diagnoses include: demodex (a skin scraping should rule it in or out), vasculitis, panniculitis (sterile or infectious but quite rare, and bullous or mucus membrane pemphigoid (which are autoimmune skin diseases). Aside from the first one I mentioned, these others would require a biopsy to confirm.
If this were my case since she's responsive to steroids, I'd keep her at the high dose for a longer period of time before slowing tapering which might be 25% reduction of the initial dose for several weeks, then 50% for 1-2 weeks, then 75% for several weeks and then every other day for several weeks and then stop. I realize that every vet has their own protocol but this one has worked well for me for the few cases that I've seen.
I hope this helps. Deb