Like previously said, it's totally time for bushings. Easiest way to tell for clunking over bumps is to bang on the sway bar in different spots. If you hit the sway bar with your hand where the links attach and it clunks, your end links are shot. If you hit the sway bar in the middle by your engine or the axle then your bushings are shot. I know 100% your bushings are shot as you should not be able to move it side to side at all. There is an actual lip on the sway bar that prevents the sway bar from moving side to side when the truck is moving. I noticed on my truck that the rear bushings were egg shaped from being worn so bad and the fronts were just rounded over on the outside edge. The front's were not in bad shape but I figured since I was doing the rears, why the hell not just do the fronts too, ya know? It is a super easy job to do. If I can recommend something and if you have the tool for it, I recommend using some long extensions and an impact gun to get the nuts and bolts loose for the sway bar bushings and do them both at the same time. Some say to do one side at a time so as to avoid shifting the sway bar from one side to the other and messing up the alignment of it but it is so much easier to slide the new ones on and off with both bushings disconnected.
I also recommend using something like PB blaster or your personal choice in penetrating oil to assist in getting those rusted studs loose. Trust me, it is possible to do it by hand but the bolts on mine were so rusted that I could hear my wrist cracking every time I moved it. haha.
Finally, I also recommend using something like wd-40 to assist in getting the front sway bar bushings on. I know some others will say not to use that on the bushings as it can cause premature wear but i'll tell you my problem. The rear bushings are super easy to spread open and fit on the sway bar. The front bushings are damn near impossible to spread open and fit on the sway bar itself. What I did was install the bushing on the outer part of the sway bar and spray some wd-40 on the inner part of the bushing and slide it into position that way. Once I got close to the position the bushing should rest in place at, it was next to impossible to move so I know the wd-40 ran dry from me sliding it into place but just my little tip on that.