[mrein3]

If you are getting to where you think the heater core is plugged, you can take the heater hoses off and flush water through with your garden hose. With no heater control valve in the way, house pressure water should flow through freely. You can remove your heater control valve if you have one for this test.
Heater cores are a bear so you want to be sure it is plugged before you go swapping it out.

If you end up swapping in a new heater core, order new heater hoses. They are cheap and easy to do at that time.