Screeching sound from engine

I can pretty guarantee you it is your altrnator belt.. By turning on your headlights, it creates more load on the alternator, which in turn makes the belt work harder. To confirm, you can try some silicone spray on the belt. The noise should change or disappear. This happens a lot in winter when dirt gets on the belts.
Usually that will solve it. If not, you may have to get the belt changed.
Good luck,

Dan

thats because you drive an eclipse!