Hello hope you are doing well. Use of heavy makeup and cosmetics can lead to dry itchy skin. The skin can start peeling. Underlying skin conditions, dermatitis, eczema and psoriasis are few other causes related to these symptoms. I will advise you to consult a dermatologist or an ophthalmologist who specializes in dermatological issues. Your doctor may prescribe topical medications to stop flaky peeling skin. If there is any doubt of infection antibiotics may also be given. Do write to me again on how you are doing.
Take care and regards!