I rescued a severely malnourished dog, and always put meat on his dog food to help him catch up, and i still do to this day. I have zero problem giving him some scraps of whatever protein we are eating---beef, chicken, eggs, fish, pork, whatever.
Hills dog food is one of the absolute WORST dog foods out there.
It is chockful of corn, is mostly corn, which is an allegren to some dogs, has zero nutrition (dogs do not digest corn) and is only a filler.
Corn is the #1 ingredient in that dog food.
The next ingredient is CARDBOARD. yes, actual CARDBOARD, "cellulose"
followed by
peanut shells!!! come on, that is the bulk of that dog food, and it's alll just crap.
The next ingredient is "chicken BYPRODUCTS", which is things like beaks and hooves and claws, not meat.
I'm not judging you, until i rescued a severely malnourished dog, i also knew NOTHING about dog nutrition, and just thought, geez, if my vet is selling it, or, if it costs a lot, it must be good dog food. WRONG. Wow, was i surprised.
(btw--------your dog's skin problem *might* be result of malnousihment, never having had enough nutrients to have healthy skin and fur). I'd add itty bitty half teaspoon of cannola oil to every other bowl, and on alternate days, i'd add busted open fish oil pill. Dogs need some fats to have nice fur.
Here are some threads on dog nutrition:
http://www.dogtrickacademy.com/members/forums/threads/i-love-to-talk-nutrition.3464/
http://www.dogtrickacademy.com/members/forums/threads/how-to-spot-great-dog-food.3308/
WATCH IN THOSE THREADS (above)FOR SOME LINKS I HAVE POSTED.
I use Chicken Soup for the Dog Lover's soul dog food.
There ARE better dog foods, the "grain free" kind, but, i can't afford them,
and, all they have done is swap out oats & rice with POTATOES. Lots of potatoes. Nutritionally, potatoes and oats are very similar.
My dog can't do large amts of potatoes, he gets gas on the grain free (potato) kind.
Chicken Soup lists FOUR meats as top ingredients, and two are in meal form (meal is good, means it is already partially dehydrated). That is hard to find, only Origen lists more, but, i can't afford it.
Chicken Soup has no toxic poisonous preservatives, NO corn, NO soy, NO carboard, NO 'byproducts', NO "animal digest" <---that means poop, NO wheat, NO proven carcinogens (YES, THOSE ARE ALLOWED INTO DOG FOOD), NO brewer's rice <--that is like peanut shells, NO controversial ingredients.
and it DOES have plenty of meats, probiotics, antioxidants, omega 3s and 6s, flaxseeds, etc.
It's MADE IN AMERICA, never gets recalled,
and
it's only a dollar a pound. You have to order it online, OR, go to your local pet supply store to get a bag, but, your dog can go in there WITH you!!
If you decide to swap out your dog food,
do so slowly, only a few kibbles at a time, and donate rest of unused dog food to local dog pound.
I am extremely extremely leery of putting dogs on drugs, unless it is last resort. First, i'd try giving this dog an actually nutritious dog food, i'd definitely supplement it with real meat, the more the better, actually, and give the dog a chance to be actually well fed, prior to putting him on any drugs, if i could avoid drugs.
GOOD LUCK, CONGRADULATION ON NEW DOG, AND GOOD ON YOU FOR RESCUING A DOG!! YAY!!!