On the subject of swaying, you should NOT be experiencing ANY sway even without any sway control.
First thing is you should determine if you actually have sway. A little bobble here and there is not sway. Any push-pull you feel from large vehicles passing is not sway. In a nutshell, anything that self-corrects is not sway.
Good sway control and weight distribution does help in these situations by keeping the truck and trailer more as a solid, rigid unit rather than an articulated combination of two separate vehicles. The truck and trailer are showing a "unified front" to the passing vehicles, rather than acting separately.
If you are experiencing true sway, all is not lost. At this point you have not loaded the trailer to camp, so it is a bit light on the tongue (barely 10%, most travel trailers need more). Once you've settled in, the trailer should have significantly more tongue weight, more in line with the 12.5% "ideal."