After a cold start, I hear this weird dentist drill kind of sound from under the hood that goes away after a few seconds, I know it's not the serpentine belt.
Hi there. The noise sounds like the serpentine belt is slipping. Try removing the belt and see if the noise goes away. If the noise goes away, then either the belt is worn and needs replaced or the tensioner is not holding the belt tight and needs replaced. The only other thing that could be an issue is the bearings are wearing and have a lack of oil on startup. If you need further assistance with a high pitch noise on the engine, then seek out a professional, such as one from Your Mechanic, to help you.