If the red spots on the chest and back are not accompanied by other worrisome symptoms like fever, itching, warmth, or discharge, it may not be a cause for concern. It is important to monitor the overall condition of the person, such as their activity level and general health. Using a gentle, fragrance-free moisturizer after bathing can help with dry skin. If the person has a history of eczema and is developing dry patches, a cortisone cream may be needed for a short period to calm the flare-up, followed by moisturizer for prevention.