Okay this may sound a little outrageous, but is it possible you can start out with just a few minutes at a time and then increasing gradually?
Is there a mental health clinic that may have a bulletin board with adds or pamphlets that you can put a little add up that you are looking for someone that would be willing to do this a few times a month or even a week? Can you even check with Social Services? Maybe once you get more settled in your new area, and meet neighbors or make some friends (try to) you will be able to talk about the kind of car ride help you need.
As an alternative would taking a local bus to places around your town help, or maybe it isn't the same as being in the car.
Just some things I was tossing around in my head for suggestions. I do not know much about if there is a type of therapist just for phobias that can help you with this particular problem but check with a local mental health care provider for some suggestions or referrals.
BTW Welcome to our website, you are about to meet some wonderful people, make friends, or just chat, who are really helpful with their support and suggestions

Take care,
DE

In giving advice seek to help, not please your friend
SOLON