Definitely sounds like the heater core.

To check everything else out.

1. Locate the 2 heater hoses on the firewall and remove them from the nipples.
2. Follow the hoses to the back of the engine by the alterator and remove one hose from the outlet.
3. Put the remaining hose back on the outlet. You have now made a loop and bypassed the heater core.
4. Fill system up with coolant and bleed system. Let it run and come up to operating temps and check for any other leaks or damage.
5. Good Luck