Engine oil and coolant mixed in radiator and engine

First check the condition of the transmission fluid. Engine oil and coolant mixing is not very common. Transmission fluid and coolant mixing is common, especially on GM vehicles. Your truck came with the red Dex-Cool antifreeze that GM advertised as "lifetime" antifreeze to make their cost of regular maintenance appear to be lower than that of their competitors, but then they put a sticker under the hood that says to replace it every three years. Even the Dex-Cool company does not recommend that. Just like with other brands of antifreeze, the additives wear out in about two years. Those include water pump lubricant, seal conditioners, and most importantly, corrosion inhibitors. When these wear out, acids build up in the coolant that attacks the metal parts. This is where GM owners have a lot of trouble leaking heater cores and radiators. The transmission cooler is built into one of the radiator's tanks, and when it corrodes through, those two fluids mix. You will find the transmission fluid turns a cloudy pink instead of the normal bright dark red.

If this is what you find, replace the radiator, then have both systems flushed and refilled. Antifreeze will melt the soft first layer of bushings in the transmission. That can lead to parts moving away from seals, then there will be shifting problems that will require a total transmission rebuild.