Our puppy vomits from time to time too.
Try elevating his food and water dishes, this has helped him not to vomit after he eats or drinks - which was suggested by our vet.

He will often vomit when he's playing with my brothers dog. They get so hyper and running all over, he'll get sick, then keep on playing.

At first, when taking him for a car ride, he'd get motion sickness. Not anymore though, he's used to it and loves the car ride. He's 6 months now.