2003 Dodge Ram no heat

I had a heater core replaced, the old one gave plenty of heat but started to leak, since I replaced it, the heat last for two min. I've had it in the shop 4 times now and they keep telling me the core is getting clogged, i've replaced three radiators, thermostate, water pump and now the third core. No problems with the heat untill all these changes were made, the Mechanic is trying to sell me on the fact that it coming from the sediment on the bpttom of the engine, could it be from the aftermarket replacements? HELP ! IM GOING BROKE Real fast. Thank You