There is a swaying in thr rear end of my 99 jeep grand cherokee Laredo

Unlike other Cherokees, you have coil springs in the rear, not flat springs.
Coils tend to react more to side loads and will therefore sway on turns more than a flat spring will. You need to look at the attachment arm bushings and mounts to make sure nothing is worn or loose.
Its very likely that the only thing wrong is that your shock absorbers are worn out. From the outside even ones that have failed don't look bad as the failure is internal.
When buying shocks, get the best ones you can afford. they last longer and control movement better. The more expensive ones tend to have larger pistons and better internal valving that translates into better control and longer life. If you carry heavy loads, I'd consider getting "coil over" shocks that also offer a bit more load carrying capacity.

Check for broken or weak shocks - low tires or a broken 'sway bar' -