It is very likely that the bearings in your fan are failing. You probably need to replace the fan.
It's purpose at that time is to keep air moving over the AC condenser. The AC condenser is located in front of the radiator. The high pressure side of the AC would overheat or would develop too high a pressure if it were not cooled by airflow when the AC is functioning.
Could be a faulty fan motor and/or switch.
You can turn the temperature of the AC up but if you turn the fan part of the AC up "high" or "low" it will only make it colder.
The 2004 Chevrolet trailblazer air conditioning fan switch has three settings. The switch can malfunction, and only work in the high setting.
Why does your ac and heater fan turn off and on
If the fan runs in high but not the other speeds the resister is bad. Done.
Broken fins in the fan or a bad compressor. Or leaves and sticks stuck touching your fan for the ac side (assuming you have a separate fan for ac which you might not).
AC
is AC, bro...
On most vehicles, it only runs when the temperature is high enough or the ac requires it.On most vehicles, it only runs when the temperature is high enough or the ac requires it.
A fan.