idle bouncing back and forth and no cold air IS related. you could quite possibly be sitting at a low charge in the AC system. The reason this happens....your AC compressor kicks on, builds up some pressure in the system, then the low pressure sensor indicates to the compressor that there isn't enough pressure, so the compressor turns off. It's a nasty cycle and will continue to repeat itself. i know this to be true because i just went through this with one of my cars.

There's a way you can do this on your own, If you feel inclined to do it. First, check under your hood to see what type of refrigerant your car is equipped with. should be 134A, but could possibly be R-12. R-12 is the outdated old refrigerant but is still used. VERY expensive. 134A is cheap and easily availible. i went to an autoparts store and bought a charging kit. bout $30. comes with the pressure gauge and bottles of 134a refrigerant. very easy to do yourself. instructions are in the kit. the refrigerant should also have a lube mixed in with it, which makes it easy on your part. hook up the gauge, run the AC system, read the pressure. if it's low, begin filling per instructions on the kit.

If your car happens to be equipped with R-12 refrigerant, you can buy a conversion kit, but it kinda means you gotta discharge the old refrigerant somehow. i doubt your car has R-12, my 96 DX has 134a. i believe in the early 90s they changed over to 134a. my 91 blazer had R-12, but i converted it myself.

your idle will naturally kick down when the AC compressor is running. when it's not running, there's not much resistance on that pulley, but when it's running, the clutch inside engages and it's one more thing the engine has to work to spin.

If you are in doubt of charging your system yourself (it is easy), take it to a shop. If you need extra info, PM me and i can give you a call and help you out.