If you're not sure if you did it "right" prolly didn't 'FLUSH' the radiator, prolly just emptied it and refilled it.

I'd get your fans in working order and jumper the main radiator fan to make sure its always on when you turn on your ignition. (that saved my arse a ton of times with over heating)

Your issue sounds like one i used to have in my old 93 civic, sitting at a light, heat temp would raise, but once moving would be aok. My tempature fan switch kept faulting and would not make the connection to turn on the fan. so i said flip it, and jumpered the fan to be always on when the car was on. Solved that heating problem.

What the year / model of your vehicle? Might be time to look into replacing the radiator / hoses as well.