Nope the Second Amendment is pretty clear on guns, not so for cars, or horse-drawn carriages, if you want to go back that far.
its also pretty clear on owning private property, which is what a car is. by your argument, you have no right to own or live in your house, wear your clothes, etc.
Can you just imagine the Founders sitting around discussing the Constitution and Bill of Rights when someone brings up the idea of listing the right to travel about on horseback or horsedrawn carriage?
They'd have been laughed out of the room. No one would ever dare to restrict your right to travel or call it a privilege.
It's one of those pesky unenumerated rights. It's our by virtue of being here.