Cooling problem

Hello, I'm new here, names Mark. If this post is in the wrong section, I apologize. As you can tell from my name, my truck is a 2000 Pete 379. It has a Cat C15/475hp engine, and it's having some cooling issues. I recently had the entire cooling system flushed and refilled because it was overheating while under pretty much no load (bobtailing). When I got it back, it seemed to cool very well, but as soon as I hooked it to a trailer, it started getting too hot again, even with the engine fan turned on. With nothing in the trailer, it does ok, still gets hotter than it should but doesnt turn the light on. Fully loaded, it's almost as if it has no water, but it is plumb full. And as soon as I stop or slow down and it has relatively no load on it, it cools down fairly quickly. The radiator, intercooler, and condenser are all pretty darn clean. Any ideas? A friend of mine said the water pump could be about to crap out.