Tell us more detail about your "sway". For your truck and size trailer...something isnt right.
I wonder if you feel the rear of the trailer wiggle vs actually sway. If its actual sway, then your weights need to be checked, most importantly tongue weight and gross trailer weight.
My trailer "wiggles" in certain situation, but never sways. For long distances, I felt things could be better, so I bought a Hensley hitch (Propride is their comp...which I wish I had bought instead). It does in fact improve the best towing travel trailer bumper pull rigs, but at a very high cost, higher maintenance, and other trade offs.