As mcarter and Jim&Cheri already said, properly using a friction sway bar will eliminate the sway.
Unless you are towing with an undersized tow vehicle (and you aren't) and aren't balancing your trailer incorrectly, you should have no need for a weight distribution hitch, given your tow vehicle.
This right (passenger) side away bar will do the job - and you can easily mount it on the trailer tongue yourself.
https://www.amazon.com/Eaz-Lift-48380-Right-Passenger-Control/dp/B007HRIVMI/ref=sr_1_1?ie=UTF8&qid=1505441765&sr=8-1&keywords=eaz+lift+right+friction+sway
It also contains a 1" ball that will need to mount to a 'tab' on the passenger side of your hitch receiver... if you don't have the "tab" or prefer not to weld a "tab" on, you can mount this plate to your hitch receiver and then mount the 1" ball to the plate (see the picture in this link)
https://www.amazon.com/Eaz-Lift-48386-Right-Control-Adapter/dp/B003VAX5NA/ref=sr_1_7?ie=UTF8&qid=1505441152&sr=8-7&keywords=eaz+lift+sway+bar