There is such a thing as a ketotic rash, it can happen if you are ketotic and sweat . google it and you will find references.
I currently have to wear a sling ( long story told elsewhere lol) and I've noticed that it makes my arm very hot and my elbow inner joint itch, which I am putting down to ketosis.
they might be some variation of psoriasis or eczema - I should get it checked out by doc.
- mind you, I have always found that is good for a diagnosis, but hopeless for treatment.
Mr B was prescribed a steroid treatment for his skin (very similar to your description), and the doc left it at that.
2 years of regular repeat prescriptions later, we discovered it was completely cured by a simple dietary change (less cheese!)
A bit frustrating, really, because the doc never even suggested looking at diet.