Peanut allergies usually develop during infancy and early childhood. Symptoms in babies include a rash like eczema (which can be seeping and crusty) or hives (raised red bumps). Babies with peanut allergies may also have digestive problems like diarrhea and vomiting. As your baby gets a little older, peanut allergy symptoms may include fewer rashes but may begin to include shortness of breath and a runny nose. Talk to your child's doctor if you notice these symptoms.