I recommend you see a different vet for a second opinion. Filou had coccidia some years ago. He had blood at his bum and I was very scared. I forgot what meds he got but he was ok in no time.
Coccidia can come with raw meat, so watch the diet as well.

I wish you all the best for Skinny. Filou is only 7.5 lb and Skinny should not try to compete with the 16 pounders if he is meant to be a slim kitty