When you say you can shake the u-joint, do you mean like up & down, side to side? If so, better get a new one. It might turn a bit when trying to rotate the shaft, but it should not rattle.
Also, if your dropping the shaft, might as well get the other u-joint while it's out. Your going to have it dis-assembled anyway & the joints are like $25.
Tire might just be loose nuts. Had that happen before. Check that 1st. Loosen them, jack it up, then tighten. drop the truck & tighten the rest of the way.
Walter