Agreed, it's motion-sickness, and he's vomiting just like a person who gets car-sick does. (parrots give you the lovely, added-touch of flinging the vomit on you/at you, gotta love them)...
Very good advice by SunnyClover about keeping your bird on your shoulder whenever he's in the car, as this is pretty much prevents motion-sickness completely. I was warned by my Senegal's breeder that he had vomited several times in the car, inside his carrier, while being taken back and forth to his Avian Vet, and that was only a 20-minute car ride for him...I was really worried about his because his breeder was in Raleigh, NC, and I was driving from State College, PA, lol...9 hour drive one-way...uhg. I brought along one of the dog carriers that I have modified for my birds, complete with a perch and a water bowl inside them, but I figured that I was going to have constantly stop at rest areas on the 9-hour drive home to clean him up and clean out the carrier...Well, I didn't pick him up from the breeder's house until around 9:00 at night, so i decided to get a motel room in Raleigh, and little baby Kane ended-up sleeping on my chest in the motel room all night long, I woke-up the next morning to him laying on my chest like a little, green fluff-ball, staring at me with the cutest smile ever. So I fed him, fed myself, and decided since he was already so tame and comfortable with me that I wouldn't put him inside the carrier for the drive home, I'd just try him on my shoulder...Well, I was wearing a hoodie, and Kane immediately left my shoulder once I started driving, and climbed to the top of my hood, so he was sitting not inside my hood, but on it, so he could see the road looking over my head, lol. He stayed there for the entire 9-hour drive home, we stopped only a few times for me to pee, not for him, and he didn't vomit once.
It's just like trying to keep a human from getting car-sick, they need to look forward towards the front of the car, never backwards, and they need to be able to see the road and the cars driving past them. If they are inside a carrier that is sitting on a seat, and they can't see anything but the carrier is constantly moving/swaying/bouncing, that constant motion without being able to see the car moving is what is making him sick. And even if you don't have him in a carrier, but rather he's sitting on a seat or anywhere in which he isn't facing-forward and where he can't see the road, he's going to keep getting sick.
I don't know your bird's personality or your relationship with him, but if he's tame enough and likes to sit on your shoulder, then that's the first thing I would try on your next car ride with him, and see how he does. Obviously if he's not tame, won't stay on your shoulder, or if he bites you/your ear, etc., then you can't do this, because the last thing you want is to wreck your car. You obviously can't have him biting you or flying all over the car while you're driving, so if that's the situation then you have to approach it another way.
I actually made a bird perch "apparatus" out of PVC that goes over the headrest of the passenger-seat, and once it's placed over the headrest it moves very little. It allows the bird to sit on a PVC perch that is up high on the seat, and allows the bird to look right out the front windshield and the passenger front window. You can make one of these for less than $10 at Lowes; the only tool you need to own is a hand-operated PVC tube cutter, which Lowes also sells for about $10. You can make them with or without built-in "bowls" for water and/or treats to keep the bird occupied on your drive (the "bowls" are made from large PVC end-caps). I'll find a photo of what I'm talking about and post it here in a minute...I made one of these in about 30 minutes, and it works extremely well for all of my birds. You just have to make sure that you bring your bird out to the car either on his Harness/Leash or inside a carrier, and then once inside the car you then get him out of the carrier and put him on the perch...I'll post a photo or two in a minute...