I have had dry patches (about the size of a nickel) of skin around both eyes intermittently. They usually occur in the summer time. They sometimes itch in the early stage and then the skin gets hard and dried out. They start to become flakey in a couple of days and have a white appearance due to the dead upper layers of skin. I suspect an allergy, but haven't discovered what food or environmental factor as yet. It could be something that I eat which is more prevalent in the summer, like fresh bing cherries, strawberries, blueberries, etc., or an allergy to cut grass and lawn mowing
An over the counter hydrocortisone cream should help, but I use Desoximetasone Ointment USP, 0.25% applied very carefully with a cotton swab. It is very important not to get any of the cream in or close to the eyes. The patch is usually gone in a day or two.