If a child has a cough after a cold, treatment can be given according to the severity of the child’s cough: 1. If the child has a mild cough after a cold, the child is usually encouraged to drink warm plain water, which usually heals itself within a week or so and does not need to be treated with medication. 2. If the cough is dry, you can take cough suppressant medication, and if the cough is accompanied by phlegm, you need to take phlegm medication. 3. The child also needs to keep warm to avoid getting cold again to avoid aggravating the cough.