1997 Pontiac Grand Prix Car barely heats and windsheild fro

I have a 97 grand prix and have been having problems with it heating correctly.

Recently, I had the cooling system flushed as it appeared really dark and brown. It seemed to have clumps too but not sure if that was just an accumulation at the radiator cap.

Anyway, now its winter here in Minnesota and the car is not heating well at all. I can see the temp rise to about 210 and then it appears the thermostat opens. Top radiator hose is hot but not super hot.

I can get intermittent heat out of the car but it's not super hot.

After running it this morning in about -5 below weather and getting it warm it was then parked for about three hours.

Upon returning the whole interior windows were frosted over.

I cannot figure out what the exact problem is. I've smelled some coolant in the interior but not always. The windows don't appear to fog either.

afterward I ran the car for about ten mintues and the car got hot, the top hose was hot, but on the heater hoses one was cool and the other was slightly warm.

I'm wondering if perhaps the core is plugged from the flush. Is there a way to flush the core or do I need to replace? Does flushing damage the core?

Any advice would be great.