What should I do if my newborn has a red rash with white tips? Ways to Cope with Baby Eczema If your baby is a newborn and suddenly develops small red spots on her face, head, chest, or back, it may be a symptom of baby eczema. Infant eczema is a very common but not serious disease. To eliminate it, parents need to pay attention to the following aspects. Keep your skin dry Eczema is associated with moist skin, so it\’s important to keep your skin dry. Mothers can update their