Be careful of over doing it on the protein. Alot of itchy dogs with problem skin are fed to much.
I have had this problem, itchy skin and split pads on too high a protein diet. My vet told me that excess protein will knock the dog's kidneys out earlier in its life than if you are moderate in the amount of protein you feed. Plus, and this is a bit of a hobby-horse of mine, I am absolutely convinced that, in dogs prone to being a bit hyper, excess protein in feed comes out in hyper behaviour.
Excess means more than needed - so that, for instance, a working collie that works on the hill needs a lot more protein than the identical collie that's a pet or does light work on a small holding.
I long ago discovered that any collie-type pet dog would do best on tinned Chappie and a plain terrier meal - probably around 11-12% protein overall. I maybe should add that all my collie-type pet dogs lived to 15 and over, and were fit and active up until near to the end.
I now have working collies - but still keep the protein in check in adults doing only light work.
The bee in my bonnet is the marketing of working feeds at pet owners - people are made to feel that they are not looking after their collie properly unless they feed a 'working dog' ration, but in fact you cannot give a pet dog enough exercise to use up all the energy and protein in such a ration. Sorry to rant - as I say, it's a bit of a hobby horse.