2001 Impala Overheating Issues

My girlfriend has a 2001 Impala. In the last month or so, her heat has stopped working intermittently. The low coolant light comes on. I filled the coolant and it didn't fix the problem. Her car will go all the way up past the half way mark and start making this high pitch whine/whistle noise from the engine and then it stops and the temp gauge shoots back down to about the 1/4 mark. I took the car a couple weeks ago and got the coolant system flushed. This did not fix the problem. The low coolant light was still coming on and off. I added coolant to the hot line. Today while driving, the heat was ice cold and the temp gauge went above half way, made that whine/whistle noise and then dropped back down to 1/4 temp. The heat started working a little. I looked under the hood and noticed that the fans wern't on. Today it was about 12 degrees F. The temp only went past the 1/2 way mark twice. otherwise the heat worked good. Later this evening we were taking the car to get an oil change and the heat wasn't working, and while we were driving the temp gauge started going up and up and it passed the 1/2 way mark, started making the noise and kept going. it was almost all the way into the red. i quickly pulled over and shut off the car. I popped the hood and checked the coolant. still full. I felt the radiator. it was hot. The fans still did not come on. I let the car sit for a few minutes and started it again. I stood outside this time. The temp gauge started going up, passed the 1/2 way mark and made the noise. The noise was coming from the front of the engine. After letting it sit for about 10min i started it up again and the temp stayed down. we drove home and still didnt get good heat. at red lights the temp would climb to 1/2 way. once we started driving it would drop back down. When you floored it the temp would go down and the heat would get real hot. What do i need to do?

Change the thermostat. It acts like the thermostat is getting stuck. You didn't post which engine she has, but the change is cheap and fairly easy on both the 3.4 and the 3.8. It is also possible she has air in the system, if the shop didn't bleed it out properly after the coolant flush.

She has a 3.4. and i changed the tstat yesterday. it was a major PITA. took me almost 5 hours. And after all was said and done All that was needed was the lines to be bleed. the place that flushed the coolant ripped me off.

When its up to operating temperature feel both radiator lines upper and lower. They should both be hot to touch. If their not after installing a new thermostat and getting the air out its probably a bad radiator. This assumes you get hot heat from the heater. If no heat suspect the water pump.
Any new thermostat get an old coffee cup boil water in the microwave then use a pair of needle nose pliers and insert the thermostat it should open.
I've gotten bad new ones before. You can check the old one this way.