Hello, this is Dr K.. Answers are not medical advice and do not constitute a doctor/patient relationship. I look forward to helping you today.
This is called exfoliative chelitis and is very tough to treat. Not many known cures. Be sure you are tested for oral thrush, yeast infection. You may want to try lactic acid lotion. There are many on the market. You may also want to try vinegar and water hot compresses. Lanolin cream may also be helpful, it is generally used for breast feeding mothers.
Hope this helps.