Brown skin on my right hand on the middle finger and has a small skin tear with no itchiness?

Need more . Information or picture. Any dryness or injury or exposure to chemicals or new soap or lotions?
Need to examine. It is not feasible to provide a meaningful opinion without examining you. You may watch and wait, if the lesion heals, that would be fine. If it does not heal in a couple of weeks or if it gets worse, it would be prudent to see a doctor.
For good health - Have a diet rich in fresh vegetables, fruits, whole grains, milk and milk products, nuts, beans, legumes, lentils and small amounts of lean meats. Avoid saturated fats. Drink enough water daily, so that your urine is mostly colorless. Exercise at least 150 minutes/week and increase the intensity of exercise gradually. Do not use tobacco, alcohol, weed or street drugs in any form.
Practice safe sex, if you have sex.

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