“Coughing up chunky phlegm?”

I have had a recurring problem for the last three years. Every winter, I get a head cold. I care for the head cold and don't feel too badly, after 4-5 days I feel much better. However, as soon as I start to feel better, I develop a dry cough from deep in my chest. It starts as a tickle, then I lose my voice down to a whisper, then I start coughing up chunky green phlegm. The coughing is also quite painful and makes my chest ache. The phlegm is green and thick and has what seem to be hard dried-up chunks of snot in it. I can't find any answers about coughing up hard chunks anywhere. What is going on? It's also worth noting that I have lived in China for four years and am particularly sensitive to air pollution and cigarette smoke.