1998 GMC Jimmy air conditioning not working

When you turn the air conditioning on--does the compressor kick in? It sounds like you have a blend door actuator that is not working,

Here is a guide to help you fix it.

https://www.2carpros.com/articles/replace-blend-door-motor

Let me know how ti goes.

Is your answer " yes the compressor kicks on and the vents blow hot air"?

I am assuming that the temperature selector switch is in the cold position and the blower only blows hot air--right?
Your heating and air conditioning systems are two totaly different systems. Your heating system relies on engine temperature to heat the coolant that flows through your heater core. Then the blower blows air right through the heater core and into the cars' cabin.
Your air conditioning system works a little different. There is a compressor that is driven by a belt mounted on the front of your motor. When you turn on the A/C switch this activates a clutch that is connected to the compressor. When activated (or kicked on) the compressor compresses refrigerant through the A/C system. To keep it simple--this refrigerant flows through the A/C system and extracts heat from the cars' cabin and replaces hot air with cold air.
The A/C system has no connection with the heating system. The pressure and amount of refrigerant ( R-134) is important. You need an A/C system pressure gauge to measure the R-134 in the system.
However it sounds like --to me-- that your problem is the temperature control switch. The switch I am talking about is right next to the fan speed switch. It has a setting that goes from "red" to "blue". Red meaning hotter and blue meaning colder. I think this switch may be broken.