If he doesn't have a fever and not congested in his lungs, it doesn't sound dangerous. Though you'll never know for sure unless you see a doctor. Whether or not you choose to give him the Antibiotics is up to you.
Personally when I get flu/bronchitis etc I hit ears, nose and throat with CS. Gargle for the throat (after swishing around in the mouth) and use an eye dropper to put in each ear and nostril. Important to hit them all since they're interconnected. And it always seems to bring some immediate relief.
No it doesn't work overnight (and neither do Antibiotics ) but for the most part seems to work about as fast as Antibiotics - and doesn't weaken your system the antibiotics do.
When it's heavily in the lungs, I'll also nebulize with CS, lobella and holy basil extract - but that doesn't sound like an issue for you.