The skin near my thumb nail is always cut and doesn't heal, is there any treatment for that?

Dry skin cracks. If your skin is dry, thickened, flaky, calloused and/or cracked then gently cleanse your skin before bed. Apply vaseline in a thick layer to your hands. Cover your hands with clean socks to avoid spreading vaseline. Your skin should be better after a week of this intense moisture treatment. If not, you might have a skin infection.