Anyone who has eczema may tell you that worse than chapped lips is split thumbs or fingers. Mine always split up along the line of the nail or along the thumb print. It hurts so much that I have resorted at times to sticking them back with superglue. It is just like someone has held your thumb down and forcibly pulled the skin apart.
Mind you, I have to sympathise as my beloved OH really suffers from a really bad split lip in the winter, so thanks on his behalf, for the tips.