1998 Chevy Cavalier Car makes beltish noise when accelerati

Noises problem
1998 Chevy Cavalier Automatic 170000 miles

This sound isn't loud, and sounds kind of like when you pull your seat belt, except from under the hood. It gets higher pitched when accelerating, and goes away around 45 mph. Also, the acceleration has been feeling sluggish, and we're thinking there's a problem with the cooling system as well, because it runs hotish, we've filled the coolant three times since getting the car a few months back, and when we looked under the hood after a 30 min drive home, the fan wasn't running, even though the car's temperature gauge was still at least in the middle. I'm very inexperienced with cars, and any help would be greatly appreciated, because I'll need my cavvie in two weeks to start commuting to school.