You catch a cold from being out in the cold or not being dressed warmly. You catch them by being exposed to the germ, usually by being with someone else who has a cold. If you don't treat a cold it will develop into pneumonia. URI symptoms do nothing to alter the natural course of the illness or prevent complications. Green or discolored mucus means you need antibiotics for an infection.
Milk causes mucus .
But sick children do sometimes vomit, and milk will aggravate that. Coughing can be provoked by irritation of any part of the respiratory tract. Most children with URIs cough from post nasal drip or mucus in the upper airways around the throat. When the lower respiratory tract becomes involved, meaning the bronchial tree and lungs which are what is in the chest, you are dealing with something more than a URI and cold medicines aren't enough. Most people with colds in social situations tell you not to kiss them to avoid spreading their colds.