Many of us deal with ultra dry skin during the winter with its low humidity inside. I have found a couple of solutions that work better than other things I have tried.
Gloves in a bottle is a lotion that dries into an impervious film that keeps the moisture in your skin. It is available at many drug stores and online. The image below has a link to the website for the company.
For those cracks in your fingers that hurt, I suggest Transpore Tape. It is available in drugstores and just a small piece of this tape will cover up the crack and not interfere with work or piano playing.