1993 Toyota Corolla No cool air!

The heater core could be blocked, in which case a cooling system flush may work. The cooling system should be flushed anyway if you have never done it.
Does the engine temp. Gauge show normal temp?

Or the switching valve and cable may not be working. If you move the lever, look at the valve on the firewall and make sure it is moving.

The engine temp. Is critical to mormal operation. A closed thermostat will cause it to overheat, an open one will cause warm air out the heater, but more importantly will prevent the engine from going into a "closed loop" where the ECM takes over fuel and ignition requirements based on O2 feedback. This can cause damage eventually to the engine and convertor by causing a rich condition.
If the switching valve is working, I would start with a cooling system flush and see what comes out.
If you see gunk and rust then that is probably your problem.

Three things you can do if you want your car to last:

1. Change oil and filter every 3000 miles.
2. Flush cooling system every 2 years/24000 miles.
3. Drain transmisssion fluid and change filter (automatic) every 2 years/24000 miles.