I can find 支气管炎 for "bronchitis" but I wonder if that's a bit too technical or medical or whether it's common in day-to-day conversation.
In English "bronchitis" is a bit technical so more often people would say "chest cold".
In case it's not clear, this is the kind of cold/flu where you cough up phlegm but don't necessarily have a runny or blocked nose, which are the symptoms of a "head cold".
I can also find the term 胸闷, but I'm guessing that might be used for much more serious chest pains?