Could I use a jack caster wheel to solve this problem?

If loading the truck causes you to drag, I'm assuming the hitch is bottoming out.

First question: are you overloaded? I don't see where you listed what you are towing with.

If you are overloaded, time for a new truck as this is only one symptom.
If you aren't overloaded, airbags would be a simple fix or depending on what is hitting, get a ball that sits a few inches higher...odds are you are too low and out of level driving down the road.