Did you recently adopt your pup? Has he been vaccinated against Bordetella? Has he been boarding, at dog daycare, or the groomer?
This looks and sounds like a case of kennel cough, an upper respiratory infection commonly found in dogs. The bordetella vaccine helps reduce the chances of your dog contracting certain strains of kennel cough but does not totally prevent it. Most kennel cough is self-limiting but your vet may want to prescribe antibiotics based on their findings during the exam and any testing performed.
Kennel cough for a dog in a home (rather than the stresses of a shelter environment) only rarely becomes a big deal, however, your dog is likely contagious and should not be taken to pet stores, groomers, etc. Also do not let him go nose-to-nose with other dogs in the vet's front office/reception area.
Seeing your vet is definitely the best route to go. However, not an emergency at this point. Unless he becomes listless, very quiet, or has a deeper cough that seems to come from the chest rather than the throat, is not eating or drinking well, or develops other symptoms.
#PetHealthandNutrition