Engine Overheating

Yikes! We need to do a block test and see if there are exhaust gasses in the coolant. Go to a local parts store and ask for a block test kit.

If the veicle was running hot and fans are not coming on that is one issue. Try turning the a.C on when vehicle is running, and see if fans come on. Either way if vehicle ran to hot the thermostat needs to be changed

Have your cooling system as well as your radiator cap pressure tested to make sure there's no leak.
Analysing your coolant for exhaust gas could also reveal if your head gasket is leaking/blown or not (which is a strong possibility if you kept driving the car while it was overheating).

You said you flushed the radiator, but have you flushed the entire system? If you haven't done that, it's something you may need to do.

Also, sometime the lower radiator hose collapses. It may look fine from the outside but be bad in the inside. You may want to take a look at it.

You could have air trapped in the cooling system; make sure you bleed it well.

Have you checked the serpentine belt and the belt tensioner? If the tensioner is weak, or the belt old and stretched, it is possible that the belt slips on he water pump pulley resulting in the water pump not performing well.

Make sure your cooling fan turn on when it's supposed to. When car starts overheating, does the fan turn on?

Make sure it isn't low on coolant. Then, I would recommend checking the thermostat. Let me know what you find.

Have you checked the coolant level in the radiator, not just the reserve bottle?

Has it lost any coolant?

It appears this may be beyond your ability. It may be time to bring it into a shop for diagnosis before you do internal engine damage.