Sounds like your pup was really overwhelmed with all that was going on. The vomitting may be a slight reaction to shots or car rides. You can test for dehydration by pinching the skin. The skin should snap back, if it stays "pinched", the dog is definately dehydrated, but of course take you new puppers to the vet if you're unsure. In the future, personally, I'd separate the shots. Don't give your pup everything at once. There are many reasons for this and I won't go into all of them right now.
Be careful of puppy classes. Some are better than others. I've seen and heard about lots of puppy classes that tend to over-excite the pups and the pup just seems to be over threashold whenever they are around other dogs. I see you're in Co, if you'd like to meet up sometime and do socialization or talk training, I have some nice dog-safe dogs. You're welcome to pm me.