Right away, I started to suspect a bacterial infection when it spread that quickly....glad you got a diagnoses and started antibiotics.
I am a big believer in salt baths. Most other countries/cultures use them. Salt and olive oil were used for centuries before soap. Once I started bathing my babies bottoms in salt water, I was amazed at how nice their bums stayed. I still used A&D, but my how nice.
Any kind of salt dissolved in warm water will work. Epsom, sea salts, table salts, kosher salts. Throw in a good handful and let baby sit and soak a few minutes. The water can be in a sink, big bowl, a few inches in a tub.