flushing a heater core

No the car does not have a heater control valve on the hoses. One hose gets hot while the other stays ice cold. I just replaced the water pump, so that shouldn't be it. The reason I think it is stopped up is because when I got the car several months ago, there were mouse nests and leaves every in the car, due to it sitting. Due to the heater core getting coolant and not leaking makes me think that it was still good, but something is stopping it up. I'll check into getting a new one; that sounds the easiest route to take.