If your heater core would leak, you would suffocate (happened to me. Fumes create a mist in the passanger compartment, first sign is condensation on the windshield, sometimes greenish from the coolant.
What could happen is that the hoses or the heater core are clogged. Then you have a problem. On one hand your heater is not working, on another, the rest of your cooling system is operating at higher pressures.
Wiggle the hoses first, check for small leaks, and then do a complete drain of system with some cleaners.
have you checked the coolant level ?Then check the heater hoses that go to the back of the firewall , if you have hot hoses going into the heater and it still blows cold air your HVAC blend doors could be not working or misaligned .