I have a 99 cavalier that is overheating.

Check your temperature sending unit plug and wiring. if there is any corrosion it can cause the signal to be out of range...If it's out of range it can delay fan start up. Works like this: sender sends info to the computer, computer sends ground signal to relay, relay completes power to the fan. If the fan works on a/c, then the fan motor is good and does not need testing. A/c bypasses auto control and keeps fan on as long as compressor is running.
Also, you can have the system tested using a heat sensing "gun" Your gauge may be off a little on the high side. Unless it is actually overheating, there may not be any problem at all.
The gun test can also detect "cold spots" on the radiator which indicate a flow problem. That too can cause your symptom. Don't forget your radiator is ten years old and likely is nearing the end of it's service life. Internal blockage of core passages is common on older radiators.
As long as you have no external leaks and engine internal gaskets are good, something here has got to help!
Good luck!