Hi Mark, this sounds almost identical to my friend's cats symptoms a few weeks ago.
He started off not eating, and his gums were very inflamed, so he had a weeks worth of antibiotics. He then started sneezing, went back to the vets, and his throat also looked sore, so the diagnosis was flu, so he had another bout of antibiotics. I don't think there was any mention of steroids, although my friend's cat is FIV so maybe that may have had something to do with it?
After a week or so Frank stopped sneezing, and although he is still a little bit quiet, he's getting back to normal. I don't think there's been any further issue with his gums though.