So I've noticed for awhile now when I turn left or right, and hit a bump or manhole cover for instance, it feels like the axle is moving left and right. Am I tripping or what?? Is there something that needs to be fixed or is it just one of those things that happens?

 

Could be wheel hop from worn shocks or the leaf spring bushings are bad. Worn shocks will cause the truck
to continually bounce when go over a bump, will feel like riding in a boat in waves. Good shocks will stop the oscillations immediately.
Usually when spring bushings go out there will be a lot of squeaking noise from the rear when going over bumps, but may be inaudible
to road noise. When parked, hop on the rear bumper and bounce up and down to see if you hear anything.