I am with Barney, if it towed fine before it isn't a tongue weight issue.
A new truck, even if it is the same brand, will be different than your old truck. Make sure your hitch is adjusted properly. Simply moving the head up (or down) might be a good way to have the trailer ride level but that alone does not help your weight distribution issue. Read the directions on the hitch, or call the manufacturer, and follow them for setup. Go to the scales and weight the setup to make sure that you are returning enough weight to the front axle. Light front ends combined with P radial tires that are under inflated is a recipe for sway.
Are you experiencing sway or just a squirmy feeling? My original P radials on my Tundra required that I air them up to the max and that really helped.