I wouldn't think it's parasites causing these symptoms. Kennel cough is a possibility, especially if the pup has just received a vaccine for this. Just going by your post, I would think it's more to do with new carpet, though. Here's some info you might want to look at.
http://watoxics.org/files/carpet-fact-sheet
Keeping in mind that a pup has its nose close to the floor and are always sniffing around and it's easy to see how the carpet could be the cause. Your post says that it's worse on the carpet than off so that might be your answer.