do I need new shock absorbers?

as was mentioned before ....the shocks are most likely not to blame.

if its sitting crookid your going to want to look for (if air shocks) as was mentioned leaking lines or bad fitting, sprung torsion bar,weak leaf springs,broken leafs , broken shackel, air pressure in your tires of course,and so on and so on.

as for replacing shocks in pairs.....I always atleast replace 2 at a time (fronts or rears) ....if you have one with 30,000 miles on it and one brand new....you may notice that you get a slight leaning sensation when hitting certain bumps due to one shock being stiffer than the other.

also, if it has a hitch on it .....the shocks have probably seen as bit more use than just from daily driving and depending on how many miles are on them...it may not be a bad idea to change them just for the heck of it BUT I doubt it will fix the problem you speak of.

good way to test your shocks is to put your weight on the back bumper and push up and down and try to get the car bouncing....if it bounces a bunch then the shocks are probably worn but if its tough to bounce let alone push down in the first place than your shocks are still probably in good shape.

sorry for the long message lol