My cars been overheating for a while, the water pump was leaking coolant. Gasket was in bad condition. Replaced the pump last weekend, no more leaking coolant. It's been about a week now and haven't seen a drop of coolant in the driveway, coolant is at the same level I filled it to, almost completely full. Hard to see since it's 12 years old and not clear, but the overflow tank appears to be at the correct level. For the past week it's been running okay, but the temp slowly started to go closer to 210(understandably though, it's been hitting 100-110 every evening). All of a sudden today it was sitting at 210 at the gas station, got on the highway and sat in traffic, and it started bobbing between 220-redline with fans on at all times, never going below 220. Was going up and down but staying higher most of the time.

Came home, let it cool down, checked under my car, around the engine bay, around the thermostat, around the coolant elbows and water pump, I don't see a drop of coolant leaked. Maybe I'm just missing an area to check. I did bleed the system using the coolant bleeder screw on the thermostat housing. Waited for a steady stream of coolant.

I can't seem to think of another issue that wouldn't have presented until a week later. Radiator, fan, pump, etc. would have shown as soon as I replaced the pump right? And no coolant leaking for a week when leak was practically pouring coolant before means the pump is sealed fine so fixed that problem. Suggestions? Should I get the coolant flushed/bled professionally to be safe? Could there be a bigger problem?

Car - 2003 Grand Prix GT 3.7L N/A