I sense a diff rebuild. What I think is happening is your diff is so worn out that it defaults to one wheel peel when you spike the gas. This causes the truck to pull. It might also have a sticking bearing on one side, either in the hub or at the diff, which is forcing the diff to unload.

A temporary drive-around-it solution would be to smoothly roll into the throttle. This won't overwhelm the diff and should help it track straighter.

A permanent solution would be to overhaul the diff and replace all the bearings from the diff to the wheels.