Whining on a 2002 Cavalier.

If it whines when moving and not moving with the engine running,it may be the fuel pump.

Possible bearing in one of the drive pulleys. I have changed numerous alternators for this noise. Take the belt off and start the car. If the noise goes away you know it will be pulley related and not transmission related. If noise goes away, spin all pulleys by hand to determine the defective/noisy one

Most whining sounds come from the belt area and are caused by a bad bearing in a pulley. You can remove the belt and start the car to see if the noise goes away. If it does, you need to spin all the pulleys by hand to check for roughness/looseness.

gears are going out

Try this have your transmission fluid and filter changed if you have not had it done in over 50,000 miles. Whining is a indicator that the fluid is getting dirty.

Could be your alternator or a bad idler pulley. Is the transmission good? It may be the tranny or your differential whining.

When manufactured (new) the rear end gears are preloaded (tensioned) and the gears are aligned. The 80/90 weight gear lube is intended to help maintain that set of adjustments for 50 - 100 thousand miles (US cars) or 150-200 thousand miles (Japanese, German, Korean cars). Beyond the design limits, gear lube needs to be flushed out and new added. If whining continues, the gears have warn beyond design limits... and will fail. Exactly when failure will occur depends on the strain placed on the gears (racing, hard acceleration, towing, carrying heavy loads).

Summary: Whining is preload and alignment ware. Good lube and gentle driving will extend the life of the differential - but no one can predict for how long.

Loosen and remove the Alternator belt which may be a serpentine belt and see if the whining goes away.
It could be the alternator or the water pump if it's driven by the same belt. It will go away while moving because the engine noise is usually negated by road noise etc but it's probably still there.

You rear planetary set is worn from a restricted cooler.

I had the same problem at about the same mileage. Replaced the power steering pump and the start up screaming went away! ( The Jeep's and mine!)