Most likely this is the "Fresh Air Intake" door malfunctioning; rear AC's normally do not have the ability to draw fresh air, and normal AC system have fresh air intake that draws hot air from outside.
I have the same problem with my 93 Chevy suburban also, and I found that the rear has a separate heater core located behind the rear right wheel well. From what I understand you have to locate it, and test it, and then flush it if the hoses are clogged.
Most likely the rear expansion tube or valve is defective.
Start with flushing both heater cores. The rear one may be plugged with crud.
If the instrument gauge fuse blows on your 1997 Suburban, you might have an issue with the wiring. An exposed or grounded wire can cause the fuse to blow each time the panel is engaged.
You have a bad fan clutch..............
Could be hi-speed fan relay or secondary winding in blower motor
check your PCV Valve
the system is probably out of coolant.
my chevy blazer 1984 the air conditioner blows from down side only.
That is normal, It is a thermostat
Heater core changed three years ago,I changed Thermostat Heater still blows cool air.
Usually is a vacuum problem. The vacuum works through the climate controls to make the vent doors open and close.