Gotcha. So the coolant level is fine.
I doubt your heater core is the problem, although on certain cars, depending on how the cooling system is set-up, a plugged core can cause both your issues. I seriously doubt its that though, especially since you said you flushed it a while back.
If you are hearing a grinding sound from the water pump, I would start there. Even if it isn't leaking externally it can be failed. That bearing can fail, causing your noise, in some cases the impeller of the shaft can come loose (therefore not pumping much), and in some extreme cases the impeller can just rot away (doubt its that one..).
Before that though, I might check to make sure the radiator isn't plugged up completely. Disconnect the lower and upper hose and using your hand as a sort of seal around a garden hose, stick the hose in the upper neck and see how forcefully water comes out the bottom. Just to be safe.