What should I do, as I swore falsely by Allah that I did not burn the car after I had done so out of anger?

This is an oath taken intentionally on a lie, and it is a Ghamus oath, considered one of the major sins. There is a difference of opinion as to whether expiation (kaffarah) is obligatory along with repentance or not. The more cautious approach is to combine both repentance and expiation. Compensation for the damaged car is obligatory unless its owner forgives it.