"I have a finger and a wrist that have dry patches and it's very itchy?"

Based on your description, it sounds like you may be experiencing dry and itchy patches on your finger and wrist. It is recommended to hydrate your skin with a fragrance-free moisturizer several times a day, especially after washing your hands. Try using a gentle soap and patting your skin dry instead of rubbing it. Protect your hands with gloves when handling chemicals or doing tasks like dishes. If the issue persists for more than a week despite these measures, it would be best to consult a doctor for further evaluation.