All fans will make a "whooshing noise"
If there is a squeaking or grinding noise the fan motor needs to be replaced/refurbished.
The engine cooling fan clutch could be locked up.
No, I have had to replace mine numerous times, and have never had abnormal noise.
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You need to have the fan replaced!!! Make sure to get one from Chevy because it is an OEM product... Don't get a rebuilt or replaced from your Schmucks.
Bad thermostat, radiator, improperly working fan.
loose or glazed fan belt.
was there something on your dash that fell in the vent, a bad fan will make noise all the time.
if fan make a loud noise your fan clutch is bad
It is the fan blower for the engine cooling system (Radiator)
It may not be the fan making "more" noise when you turn on the lights. It may actually be the bulbs making noise. Incandescent bulbs when operating on a dimmer make a high pitched noise - it is the filament vibrating. Try just the lights without the fan and see if you hear anything.
the radiator could still be warm or if the car is cool and it runs you need to replace the fan relay switch.
Loose or glazed fan belt?