Every Time I Get A Cold, I Get A Lingering

Every time I get a cold, I get a lingering cough which is debilitating: Choking, gagging to the point of nausea. Also sore ribs. Rarely does my primary care MD prescribe antibiotics, only if the mucus turns green or yellow. Usually, she prescribes a cough medicine with codeine. My question is why the lingering cough occurs.
Thanks