I'd go to a trusty bulldog vet to have it checked out. When Stig had dry heaves and coughing, he caught the kennel cough bug from somewhere. And, yes, they can catch it even though they've been vaccinated for it. It's like the flu, there are just too many strains out there.
Even if it's not kennel cough, I'd still go to the vets so you'll be able to get some answers. Poor guy, must not be sleeping so well.