try to undo the overheating by using water, and if the problem solved it is not going to be permanent, you need i think to change that part,, you do not have to buy new one used one can last. good luck
1. You have not bled the system completely. The best way to do that is to get a Frease Bleeder: http://www.geocities.com/cplca/FreaseBleeder.html This company also have some other good products for that car.
2. The fan/fans are not working properly. The way to check that is to just cut the car on and let it run up to operating temperature. The PCM is programmed to turn the primary fan on when the temp reaches 180 degrees(if you have a stock thermostat). If the fan doesn't come on, check the fuse/relay. These cars have a problem with overheating relays. So, it might be a good idea to replace the stock relay with a heavy duty relay. You can get the "Fan Relay Kit" here: http://www.innovativewiring.com/ChevyProductPage2/ChevyCarsPage2/ChevyImpalaPage.htm This company also have some other good products for that car.
3. You could also have a burnt wire somewhere between the fuse/relay and the fans. Go to the same link that I just posted and look at the "Primary to Secondary Fan Harness" and "Main Fan Harness".
4. Your waterpump could be leaking. You said you put in some antifreeze. Do you have a leak? Check the ground for a puddle.
5. You could have a bad thermostat. Try replacing it.