I used to feel that way w/ anxiety too. And actually I can get a little car phobic too, if I have a panic attack while driving I get a little gun shy.
On the possitive side you know it is anxiety. (though vacuuming out the car and spraying some of that febreeze allergy reducer stuff might help if allergies are a possibility plus it will help you rationalize that it is only anxiety as you have allergy proofed your car). Does it happen only when you are alone or the driver?
I think the important thing (well what I have to do for me anyhow) is to keep driving, keep fighting and show the anxiety who is boss. Maybe just sit in your car, in the driveway, for a few minutes at a time and not go anywhere, then build up to just around the block. (obviously you will have to drive for real other times but I mean as "practice) then you can show yourself flat out its anxiety and hopefully this will make it go away (at least gradually).
Hope this helps!
\"As soon as you trust yourself,you will know how to live.\"
Johann Wolfgang von Goethe
\"Do not anticipate trouble, or worry about what may never happen. Keep in the sunlight.\"
Benjamin Franklin