Stress can indeed be a possible cause of a red rash on the thumb. It is recommended to use a fragrance-free moisturizing cream at least three times a day and after washing hands. Avoid using scented soaps and gently pat the skin dry instead of rubbing vigorously. It may also be helpful to apply the cream before going out in cold weather and wearing gloves if possible. If the situation does not improve or worsens after trying these measures for 10 to 14 days, it is advisable to consult a doctor as a precaution.