Oh, my! This brings back bad memories!
One of our chihuahuas had sarcoptic mange. The vet diagnosed it as sarcoptic mange. He said she was born with it. This was many years ago and we didn't have the internet or a lot of information available about it. The vet had a prescription formula that I mixed with water and dipped her in it. It smelled so bad.
She itched so much and she hated the smell as much as I did or worse. She would try to rub it off of her. On my own, I obtained sulphur powder and mixed it with vaseline and applied it to her. I would leave this on for awhile and then bathe her. This was not a fun time, but we got rid of it and this poor little dog that had bald spots on her grew the most beautiful coat of reddish-brown fur! She was never troubled again, but the treatment took months.