When I brought Miles home at 10 weeks old, he had kennel cough really bad. It ended up lasting a couple months, and took a couple rounds of antibiotics. Sometimes, he would cough so hard he would throw up a little, but I would check with the vet to be sure.
As far as poop goes, Miles had the weirdest poop for about the first two weeks I had him. One time it could be solid, the next time runny, other times, just plain disgusting. I just monitored him carefully (if they have diarrhea they can get dehyrdrated fast).
If I were you, I'd go back to the vet just to be sure. You can never be too careful! Good luck!
