Hi. This is called as hand eczema. This can happen because of frequent use of alcohol-based hand sanitizers and excessive hand wash. It can also happen if you have not washed the soap off correctly with some soap residue left behind.
Next Steps
Keep a moisturiser next to the basin. Apply moisturiser after every hand wash or whenever it feels very dry. You can also use hand wash made for sensitive skin. Visit a dermatologist if the symptoms increase.