A generalized staph infection is the most likely
cause of this rash. Antibiotics should be helpful.
If you feel you need immediate help in the future
your local veterinarian is the place to go.
go to the vet asap. It could be a number of things: dry skin, fleas,allergies, mange, etc. I have a pitbull that has serious skin allergies, so we give him a L.I.D (limited ingredient diet), you can try doing this, if he stops itching it has to of been allergies. We give my dog natural balance duck and potato, plus raw foods and L.I.D treats. Do not give him anything else such as dog food with wheat, soy, grains,etc. See if that helps. But the vet would be the best choice. they would do skin scrapes to find out if its mange or allergies, and they will tell you to put him on a L.I.D if it is allergies, and if its mange they will put him on a demodex treatment.
steroid treatment for allergies should be asked by a vet.
when it comes to hygiene\ shower\bath, maybe use baby shampoo(but ask a vet first!)
anyway the dog might need a more intense parasite treatment.
just go to the vet and ask about this things as well, dont try to do his\hers job, but you do have a place in bringing certain points up.
i hope there's gonna be improvement.