Does it happen at certain throttle positions? For example, when you're coming off of a stop light, does the screech start at a certain throttle position? Can you make the noise go away by changing the throttle position?

If any of those questions are "yes", try turning your throttle body idle screw inward about one full turn, and then back out about half a turn. Then gob some silicone into the screw to hold it.

You're sure it's not a loose belt? Have you tried tightening the alternator belt? Have you tried removing the alternator belt and driving a short distance (dont drive far, you'll drain the battery)? Have you tensioned the timing belt?

Try those options. When you say it's a screaming sound, does it sound like it's coming from one side of the engine bay? Or is it hard to locate?