Humm? If a cop spots you, he will write you a very, very expensive speeding ticket? No?
Ah, you want to know what happens to the light leaving your headlights? It travels away from you at what you measure to be the speed of light. It illuminates what is ahead just like it does now.
It is true that if you were instead flying a fighter jet through our skies and fired a 20mm round, it would start out at the jets velocity (cruising speed 777 mph.) plus it’s own velocity 3450 feet per second, so combined about 777 mph + 2352 mph. or 3129 miles per hour. That would last a very short time as friction with the air would begin to slow the round down. So would a light beam from the jet go the speed of light plus the speed of the jet? No. It would go the speed of light. How is that possible?
Light has its own interesting characteristic- it IS ALWAYS independent to the speed of the observer, as well as the speed of the source of the light. The faster an observer goes the more their “time” slows down from the viewpoint of an outside observer. Another thing that happens is that space- remember it and time are connected- so spacetime contracts and time slows in the direction of travel. Time will either speed up or slow down and space will either get longer or shorter so that light appears to have a constant speed through a measure of space. Because you will be affected by the spacetime in which you stand – made longer or shorter, or wider or thinner, light will always appear to go the same speed.