I agree, carsickness and stress probably caused this puppy to vomit. (regurgitation refers to the food immediately coming back up with no abdominal heaving, and indicates an anatomical problem).
What you described is "too much too soon" and may actually "flood" her psychologically so that she is now sensitized to noises and movement and fears that.
She may be a sensitive puppy and got really overstimulated. She is also in the middle of a fear-imprinting period, so pull way back on the stimulation and go slow and secure with her.
You might try just feeding her in the crate in the car for a couple days, then take a short ride for a couple days, then a longer ride (on an empty stomach) where there is noise. Then take her out of the car to a friendly, quiet place. What I have done with puppies I wanted to socialize quickly is take them into Petco in a cart with a blanket for her feet. That way she feels secure and the risk of her contracting anything is minimized, but she is getting some socialization to new things.
Sounds like you are trying to do right by your puppy, OP, understand the need for exposure, but it may just have been too much for this puppy.
P.S. When I fly puppies I try to involve the staff at the airline as much as possible, so they will check on her and talk nice to her during her transport. It's a fun departure from their normal job to oversee an adorable Lab puppy, and she will benefit from their love and attention!