Hi, keep pedialyte handy if the pup is throwing up and has d. As furparents we haaave to put our foot down with the vet. If you don't feel comfortable with something, tell him so, research it and then proceed. I refuse the lepto shot, all the time. Sometimes its best to give one vaccine at a time, get one, come back the next day, so the pup won't be "overloaded".
I hope your sweety gets to feeling better