You don't mention tongue or trailer weights, but those are important to know. A WDH helps level your truck, so your headlights don't blind oncoming drivers, and it keeps the weight properly distributed. Some will say an F250 doesn't need a WDH, but since you are having sway problems, that is one of the ways to overcome it. Not all WDH systems have anti-sway, so be careful of what you buy.
Sway can also be caused by improper loading. Tongue wt. should be 12%-15% of trailer weight. How you have the trailer packed impacts your tongue weight. You need to get your setup weighed, so you know how much your truck weighs (loaded for travel), how much your trailer weighs, weight on each axle, and tongue wt. Then, you can figure out why you are swaying.