Congratulations on your puppy and welcome!
My puppy got car sick as well the first few months we had him. Positive exposure to the car, along with short trips, are great. Take your pup out and just sit them in the car while it's parked and turned off. Reward, reward, reward. Do the same with the car running but still parked. Like Ashley, I do a lot of travel with my dogs. I gave my pup ginger snap cookies about 15 minutes before a car trip. Ginger is a natural cure for upset tummies.
Another thing I found that made a difference was the type of crate my pup traveled in. We started him out in a airline style crate (think VariKennel) and he was always getting sick. After about two months we switched him to a small wire crate and the car sickness abated. (He was also about 7 months old at the time.) For some dogs, the opposite works - the less they see the less sick they get. I mention this as something for you to stick in the back of your mind to try if nothing else is working.