Sounds more like that it is spinning when it shouldn't. This is because it's a viscous clutch fan, and when it fails, it locks up.
If you start the car when it is dead cold, it should spin up and then come off after a minute.
Or, to test whether it has seized or not, tomorrow morning, open the hood, and try to spin the fan with your hand (car off!). If it resists a LOT, then it's seized and you need to buy a new one. Changing it is pretty easy though (4 bolts), and if you wiggle it, just a little bit, (hehe) it should slide past the radiator shroud.