Cooling question for the masses

[70Custom10Nut]

Starting with a little background. I'm stationed in Germany. My truck is with my son is SC. This past winter he took the truck to Automotives class and flushed the cooling system for me. Now he's saying that the temp gauge reads that it's overheating, the heater core leaks from the bottom fitting, and the bottom of the radiator is leaking. Will a heater core leak to the outside? I've always known that coolant inside the cab floor to be the telltale sign for a bad one. Does flushing system effect the temp sending unit and/or the water pump? He's already changed the thermostat. The radiator is a no brainer, but can anyone in the Columbia SC area recommend a reliable radiator repair shop? It's kinda frustrating trying to fix things over the phone.
Any advice would help, thanks