Wow! That can get expensive. The radiator has two Transmission Fluid lines (One to send hot from the transmission as it goes through then another one to return cooler fluid back to the transmission). If any of the radiator hoses are soft or leaking, then it's time to replace all of them. Coolant reservoir should have a full mark on the outside of the container.
In my 2015 Silverado Crew Cab 5.3L, I had both fans run for 5 minutes (or longer) after turning off the engine. It was fixed by replacing the thermostat (part consists of stout hard plastic hose fitting with a thermostat inside. My first clue was the fan running fast while driving then even after turning off the engine. Look at the temperature gauge which should be straight up in the middle. With your climate, If driving is stop and go, then higher temperature coolant could be normal. Highway driving will send a lot more air over the radiator to remove heat. Check mixture is fresh with 50% antifreeze and 50% distilled water. Be sure the coolant is maintaining pressure (little below 15psi is normal) Too much pressure causes leaks. You should be able to get a pressure test kit (loaner tool) at Pep Boys, Auto Zone, or O'Reilly's to see if system is sound. Does the engine run smooth? Hope this finds you more success.