If you and your vet have completely ruled out any type of allergies, you might consider adding some salmon oil or coconut oil to the diet to help with the skin and coat dryness. I took Toki in for something similar (she wasn't itching and scratching herself bloody though... she just had dry flaky, skin on her paws). Our vet thought it might be related to the weather changing (cold and dryish now) and suggested increasing the amount of salmon oil that we gave her...we used to give her 1/2 pump of Grizzly Salmon Oil with breakfast but we upped it to a full 1 pump and that really seems to have helped us out. Just a suggestion of something to discuss with your vet
