Did you match load range of the new tires to the old tires or did you go up or down? First thing to know is that your wheel width within the tires specs, preferably matching the optimum width. Next is knowing your specific wheel weights. That would help you set the tire pressure to the correct PSI to match your load.
Over inflating the tires can cause a smaller foot print (in tire terms “contact patch”) which may be the reason for the sway. Or lack of pressure to carry the load can create a “squirm” causing the sway. Lastly, I’m assuming you installed trailer tires and not light truck tires. Typically light truck tires have a deeper tread depth then tires designed for trailer applications. This can also result in tread squirm until the initial tread depth starts to wear.
A number of years ago when Bridgestone introduced their new drive tires for semi’s, M726, it came with 32/32nds of tread. At first a number of drivers complained about the squirm as a feeling the truck was on ice. Once the tires wore down the first 4-5 32nds the truck settled down and the tires wore like iron. The 726 have been the gold standard for drive tires for years.
Lastly you may want to jack up each wheel position, loosen the lug nuts, then making sure that the wheels are contacting their mounting surface squarely, tighten and torque the lug nuts in a star fashion to the recommended torque specs.
