Heater core

Get the heater core pressure tested to know for sure, although based on your description that does appear to be your problem. There is a condensation drain inside the heater box so if you're leaking coolant from the heater core, you should see some pooling under the car, right about under the center of the firewall area. Maybe let the car run in park (revving it too) for a bit and see if that is happening.