Glad that worked for you. Now that could be all that was needed. However, your year car has the actuators that are known to go out of range. They fixed that issue in the 2001 and higher Vettes. Also, low R-134a can create the same issue that you've experienced and if your refrigerant is low, that means that you have a leak. Here's what you can do to make sure there is nothing else wrong with your system.
You can have a mom and pop shop do a "evacuation and recovery" of your system. The machine that they use SHOULD be able to not only recover and replace the refrigerant in your system, but also tell you EXACTLY how much refrigerant it recovered (the ACR 2000 was the unit that GM recommended to use when your car was manufactured. Something similar will suffice). This system also has the ability to check your system for leaks. Your year car should have exactly 1.625 lb's of R-145a in the system (.0737 kg) No more, no less. If it does not, then you have a leak somewhere and when they fill the system back up, they should insert some green die into the system to help locate that leak (all AC systems are sealed and will never loose refrgerant unless a leak develops).
Make sure that you check your codes. If your system has a issue, you may throw the B0361 and B0441 codes. Those pertain to your actuators, which you just reset. There's another code that will set if your refrigerant is low but I can't remember exactly what that code is right now. One more important piece of advice. When adjusting your temperature, DO NOT spin the temperature knob very fast. This can cause the HVAC head unit to misinterpret the action and cause you to have the same problem you just fix. The head unit cannot always properly interpret that action so turn the knob normally to slow when adjusting the temperature. So many people made this mistake that GM had to put out a TSB about it so that the technicians could pass that information off to the customers.
Stay cool!