I was in a very similar boat with Beau when I first got him...he was 9 weeks old, had a bloated tummy (which became unbloated about 36 hours after I got him after he ate a bunch of food), he had mange (Sarcoptes Scabiei) and a secondary skin infection. He had never seen a vet.
I took him to the most respected, and also most expensive, vet in the area...and she vaccinated him without any problem. Not kennel cough though, I passed on that. Just the standard stuff...distemper, dewormer...along with weekly antibiotics for the mange and twice daily pills for the skin infection. He was feeling like a million bucks in no time.
It was very rewarding to be able to bring him back into good health. Seeing him scratch and whine all the time wasn't fun. Good luck with your pup.