Hi.. Dry skin by nature has less water and fat content within it. This predisposes to a rough skin that is easily prone for irritation from external sources. The more you scratch, the itch continues due to irritation of nerves in the dry skin. When itching goes severe, it incites a reaction in your skin resulting redness and swelling. This is medical terms is called dermatitis. So it is important to treat the dry skin which is the root cause of all the problems you are having. If you were my patient, I would prescribe a course of antibiotics and topical steroids depending on the severity of present dermatitis. Once that resolves i would advise on using moisturizer thoroughly to tackle the dry skin. I recommend you to have a personal consultation with your dermatologist for assessment of problem severity and thereby an appropriate prescription. Hope i have addressed your concern. Wish you speedy recovery