for sway control, typically the rule of thumb is friction bars for under 26'. Over 26' you want integrated sway control. Reese dual cam, Reese strait line, or equal-i-zer should do just fine for you. I would get 1200 lb bars. If you want to go high end there is the propride or the Hensley arrow.
As mentioned above the sway you have is probably related to loading. Ideal tongue weight is 13-15% of loaded tt weight. Do yourself a favor and hit the scales before you go looking into a new hitch. Go to
Cat scales to find a local one. Have truck front axle on scale pad 1, rear axle on scale pad 2, and both tt axles on scale pad 3. Get 3 weights, one of just truck no tt. One of tv + tt no wdh and one of tv+tt with wdh. Ideally, you will find your loaded tongue weight to be within that 13-15% margin, otherwise you need to move cargo around to achieve that goal. Your other goal is to dial the hitch in to have your tv front axle as close to unloaded weight as possible without going heavier. Try this and see if you need a new hitch first.