Check for fleas.
Even one can cause a chain reaction rash that can get really ugly really fast.
Hans is terribly allergic to flea bites and even if one jumps on and bites him once, he has to go on Zyrtec immediately.
I swear, looking at your pics I see some tiny dots that I suspect to be flea dirt.
My vet loves Dex, too, but I find it is very much a band-aid.
Also, if the food contains chicken or any kind of other poultry, you may want to switch to another protein. Good luck.
Oh... and Penaten cream works wonders on Hans's skin rashes! It is very thick, though. You would only need a rice-sized little pinch for those face sores.