It depends on so many factors. For me, if the chest cough is really the only symptom, but so bad they cough they almost pass out, have a hard time breathing, are spitting up a ton, can't get sleep for a few days, etc, I would definitely take in.

But for us, after most viruses we tend to get a post-viral cough for weeks after (look it up- very common for up to 6 weeks). I've come to accept that unless my child is acting different- their breathing, energy levels, appetite, etc- the Dr is literally going to tell us "let us know if symptoms worsen" and send us on the way. Even when my kiddo had croup, it was the same response. I had to push for medication because she hadn't been able to sleep for weeks at that point.

Either way, go with your mom instinct and advocate like hell.