Typically the rabies shot is not given until at least 4 months of age. I am thinking the vet pushed it with your little puppy.... At 15 weeks he should have recieved the parvo shot, distemper, and one other one...
Rabies should have only been give without any others.
I have seen many members reccomend not giving the rabies until a little older..
I am sorry your little guy has been vomiting. It sounds like he has had a reaction. Keep an eye on him, and if he is still unwell by tomorrow, call the vet. AND look for a new one!