I just replaced the catalytic converter on my 03.

Catalytic converters don't make noise unless they break apart inside and rattle. Typically a whirring noise would be caused by an electric radiator fan. That should not run all the time; just off and on when the engine is hot. It won't hurt anything if it runs all the time but it will wear out sooner, and of course it had better stop when the ignition switch is off so it doesn't drain the battery. It would be smart to have your mechanic listen to it to rule out anything that could cause damage to something else. If the source of the noise can't be located while the car is standing still, there's a tool called the Chassis Ear that uses six microphones so you can listen to six suspect areas while you're driving. I can describe that better if it becomes necessary.

I would attack that with a stethoscope. Harbor Freight Tools and auto parts stores have them for about ten dollars or less. Listen right next to the pulleys for the generator and power steering pump, but the bearings in idler pulleys cause more noises than anything else.