Leak coming from under the water pump but its not the water pump on a 93 chevy s10 2.8ltr

Here's a Autozone repair guide on your water pump. Repair Guides Engine Mechanical Water Pump AutoZone com

Could be the water pump leaking.

check the drain hole under the water pump housing or check for rusted out welsh plugs . Have a coolant pressure test done and see where the coolant is coming from.

i would check the radiator hoses if they are not leeking the it would most likly be a water pump

Is the antifreeze leaking out of a small hole on the water pump housing just behind the pulley?
You need to know exactly where the leak is coming from. If the pump is not leaking then there is another location.
Generally pumps either work or leak. They do not slow down and overheat the engine.
Where did the smoke come from? Under the hood or out the exhaust pipe? If you blew a head gasket and the exhaust was blowing steam that would cause overheating. The original leak under the engine would cause overheating that then will cause other problems like blown head gaskets.
Did you use stop leak or some quick fix? what did you do to stop the original leak?

Sounds like it's leaking from the water pump. There are weep holes in the water pump and when the bearing in the water pump has worn out, coolant will start to leak from the holes.

Replace the water pump after you inspected it for any signs of leak. Good luck and thank you for using Fixya.

Could possibly have a clogged radiator, Which engine does your caprice have? You also need to make sure all air is purged from the system.

When does it over heat, all the time, or just when idling?

It is the water pump most likely,they have ,what they call a weep hole in the bottom under the pulley,so they will leak out to let you know to change them right away.If it is on the top coming from the intake area,it would be the intake,they are also bad to leak,but look at the pump,under the pulley.

You have answered your own question almost. You will need to jack the car up and inspect everything being that its 91 camara, there is defintely enough room to inspect everything. You either have a hose leak, a radiator or water pump leak. Only inspection will find that out. Thank you,
Lee

When they changed the water pump and the leak stopped then the water pump was bad. If they changed the water pump and was still leaking then then it was not the water pump. 
Where is the fluid leaking from, if there is white smoke coming from the tail pipe then good chance is that the head gasket is gone and pull the dip stick out to see if there is antifreeze mixxing with the engine oil.
It's common that the 3.4 V6 has intake manifold gasket go bad and leak. Check all the heater hose first, and try to find out where the leak is coming from.
Good luck and keep me posted, glad to help you as much as i can.