HEATER CORE ISSUE

Yes, heater core is the culprit. It requires removing the steering column and dash assembly to get the heater box out. That also means discharging and disconnecting the air conditioning system. This is a major job, not one for a do-it-yourselfer.

First check the heater hose connections at the firewall under the hood to be sure they're tight, but those will usually cause leakage onto the ground, not inside the car.

Caradiodoc

If it's leaking coolant on the passenger floor then yes you need a new heater core. Here is the instructions on how to replace it.
REMOVE OR DISCONNECT

1. Negative battery cable.
2. Drain cooling system.
3. Right sound insulator
4. Center Instrument Panel (I/P) trim plate.
5. Lower I/P trim plate.
6. Wires and hoses from programmer.
7. Programmer linkage cover and linkage.
8. Programmer attaching bolts and programmer.
9. Heater core cover.
10. Splash cover to access heater hoses.
11. Heater hoses from heater core.
12. Heater core.
INSTALL OR CONNECT

1. Heater core.
2. Heater hoses.
3. Splash cover.
4. Heater core cover.
5. Programmer.
6. Programmer linkage and linkage cover.
7. Wires and hoses to programmer.
8. Lower Instrument Panel (I/P) trim plate.
9. Center I/P trim plate.
10. Right sound insulator.
11. Fill cooling system.
12. Negative battery cable.

Your welcome that's what were here for.