1993 Chevrolet Cavalier cooling fan

Did you check voltage and ground at the fan wiring connector? How hot is the engine getting in degrees F? Some fans won't kick on till about 220 degrees F.

If you turn on the ac, will the fan kick on? You can use jumper wires from battery for voltage and ground to fan connector, just to see if fan motor will run. If it won't run, something wrong with fan motor. It wouldn't hurt to use inline fuse on the jumper, just in case.

Can you check for applicable trouble codes, your obd1 so you should be able to check some codes, yourself.

Just to add, note, part of wiring diagram cooling fan circuit. The black wire with red tracer is voltage for cooling fan, the solid black wire is ground. Also, the coolant temp sensor has some control over the fan. On some makes and models, if you unplug the coolant temp sensor the fan will run all the time, engine is running.