My dog had all of the same symptoms when I got him from a shelter - snorting, sneezing, coughing, reverse sneeze attacks, etc. I took him in for his free wellness check and the vet didn't address his symptoms and only gave me literature for reverse sneeze. He got worse and was miserable and coughing all night. I took him to another vet who diagnosed him immediately and put him on antibiotics (he also had an ear infection the 1st vet missed--sad!) By then I'd already exposed him to my parents' elderly dog, so I wasn't happy with the first vet. Anyway, my point is that it is very contagious and can progress quickly. The 2nd vet also told me to use Robitussin at night, but he threw that up so I never gave it to him again. It took awhile to clear up. I'd definitely get him to a vet and keep him away from other dogs until it clears. Did your shelter offer you a free wellness visit? Glad you adopted him!