Bronchitic belongs to bronchitis — the illness of the bronchial tubes that makes you cough. As an adjective it means of that illness, or having it: a bronchitic cough, a bronchitic patient. As a noun, a bronchitic is a person who has bronchitis, often someone who gets it again and again, especially through damp winters. You will meet it in medical notes more than at the dinner table. Though actually, the word does not name the illness itself: the illness is bronchitis. Bronchitic is only the about-it / having-it form. In casual talk people more often say a bad chest or a chesty cough.