Generally speaking, common cold symptoms include a runny nose, sneezing, nasal congestion, some may have a cough, and others may have a fever. Generally, after most babies catch a cold, the symptoms are mainly respiratory. A small part may show symptoms of the digestive system, such as vomiting and diarrhea. There are also headaches, mental fatigue, lethargy, sleepiness, etc., so there are many symptoms of a cold.