Definitely, especially if the child is not vaccinated against whooping cough
(also called pertussis).
The symptoms can be a runny nose
and a very distinctive cough (hence the name "whooping cough.") the "whooping" sound is heard on inhalation. If in doubt, see your pediatrician/family physician, since pertussis is a very contagious disease and needs to be treated right away.
Answer assisted by David Escobar, Medical Student