Possibly croup. A barky cough in a child can often be due to croup. It is a viral infection which causes swelling around the vocal cords, leading to the characteristic cough. A runny nose and fever are often associated. However, other things can cause a cough in a child, such as an inhaled item, bronchitis, asthma, a head cold, etc. If the child has a hard time breathing or it continues, see a doctor.