OOOOH! Let me know what happens with your baby! Lily was EXACTLY the same way when we got her at 6 weeks (young I know!!)--she's 12 weeks now and the cough is still hanging around. Been to the vet several times already. We've done two rounds of Clavomox, tried Primor but had a bad reaction to it, and now we're waiting it out again.
Try a vaporizer beside him at night... that did seem to help Lily for a bit. I'm thinking about going back for a 2nd opinion from another vet. Is your little one eating and drinking and playing okay? I'm also trying to give her a tsp. of plain yogurt a day now too so all her "good bacteria" isn't being wiped out with the antibiotic. I've heard all kinds of things on here... lots of good advice. Good luck!