One of the possibility for such symptoms is xerotic eczema. The mainstay of management is liberal use of moisturizers after washing with luke warm water. Soap should be used minimally. Moisturizers should be reapplied liberally during the day. You can also use a topical cortisone (steroid) cream or ointment like dermacort(hydrocortisone). Adding a humidifier to the central heating system of your home or using a humidifier also helps.
If the symptoms persist then you can get it evaluated from a dermatologist.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.