Hello, Allan
The A/C clutch is not likely to have caused the problems you describe. To find out whether it is working, you are best off with a helper.
Start the car with the engine lid open and A/C off. Look into the engine bay, and look at the A/C compressor atop the engine. It will be driven by a belt from the end of the crankshaft next to THE belt that drives the big engine fan. Normally, the compressor is mounted above the engine to the righr, when looking under the engine lid, and should have two thick hoses connected to it.
While watching what is going on with the engine running, get your helper to turn on the A/C from inside the car. There should be a loud snap and you should see part of the compressor start turning.
The snap is the A/C clutch engaging. Some time later it may disengage and then re-engage in cycles to stop the A/C system freezing.
It seems unlikely that failure of the A/C compressor's clutch could cause the problem you describe. Maybe, the compressor could have jammed - this would cause the drive belt to scream until the drive clutch was released. If this is the problem, I am sorry because the compressor is expensive to replace!
Alistair