First thing, what did the coolant look like when it first overheated. Did it look cloudy or just a clear orange? Did it turn brown?
If it was anything but a nice clear (transparent) orange, then the corrosion inhibiters had broken down and you were getting oxides in your coolant. That may have contributed to the overheating. Certainly a fan not running was a major contributor if the overheating occurred in traffic.
Changing the thermostat may not have actually solved the problem, assuming that you did not reuse the coolant and had fresh coolant put in. The problem would have been solved by the fresh coolant more than the thermostat.
But replacing the thermostat was a good idea, first because it was the wrong one and second because it is near its life expectancy and would have failed in the near future. So changing it was a good idea even if it wasn’t the actual cause, plus it actually could have been the actual cause.
Temperature gauges have gotten more accurate lately, they used to be notorious for being way off, similar to the analog clocks in the dashboards of older vehicles. The smallest increment on your gauge is about 7.5 degrees. It’s about 15 degree per the next slightly longer increment marks. So if your gauge moved up two smalle increments (one medium increment) when you went from 180 to 195, that is to be expected.
I would strongly recommend against flushing out the cooling system. Just change drain and refill the system with fresh dexcool when ever it is anything but a clear orange.