Level 1: Symptoms and causes of babies coughing and spitting up milk. It is a very common phenomenon for babies to cough and spit up milk. It is usually caused by lung or respiratory tract infection. If your baby is also accompanied by symptoms such as fever, runny nose, and sore throat, it is most likely caused by a cold. In addition, if your baby vomits after feeding, it may be because he or she ate too quickly or