I wash my hands over 20+ times a day and they get the same way. After a lot of trial and error, here's what worked for me to make the skin better. I put this on before I go to bed.

1 - Rub this specific Aveeno lotion on 1st.

2 - Put on a layer of Aquaphor next.

3 - Wear eczema gloves on your hands. You can find them here.

This is my regimen to keep my hands in good condition during the winter. I put this on before I go to bed.

1 - Rub this specific Aveeno lotion on 1st. You could replace this with O'Keefees working hands, Neutrogena norwegian formula, or something similar.

2 - Put on a layer of Aquaphor next.

3 - Wear eczema gloves on your hands. You can find them here.

I'd suggest a tub of Aquaphor -

https://www.amazon.com/Aquaphor-Healing-Ointment-Moisturizing-Protectant/dp/B006IB5T4W