One thing you might have done is a thyroid test, Becatsa. We saw dry itchy skin and excessive licking in our dogs that developed immune-mediated hypothyroidism. Treatment of the hypothyroidism fixed the dry skin problem.
Fish oil (omega-3) supplements might also help condition the coat.
And with a little luck, conditioning the skin might help with the nosebleeds
Please keep us posted on your dog's progress, Becatsa! And welcome to the board!