Has he been in contact with any other dogs? It sounds like kennel cough to me. Even sniffing in areas where other dogs are can yield a bout of kennel cough.
You might say "well, I've had him vaccinated for that!" but, as I learned with my bully, kennel cough vaccines are like flu vaccines - they only prevent certain strains but not others.
That said, the treatment for kennel cough would be a round of antibiotics so I would take your Baxter to the vet - heavy congestion and bulldogs is not something you want to mess around with.