Hello,
Drying out around the eyes and peeling and painful may be dermatitis. I've had something similar. With me, it was a kind of immune-response for which over-the-counter hydrocortisone provided temporary relief. I now wash and moisturize with completely natural products, and it works very well for preventing these flare-ups. (It may be placebo effect, but it has lasted a long time). I use a castille soap to wash and organic virgin olive oil to moisturize. I've been very happy with the results. It may not work for you, but if it does, it's an all-natural, inexpensive solution.
--Jane