You must relax your hands, hold those barre chords with as much pressure as needed to sound the strings cleanly but not more. Allow and seize opportunities to allow your hands to rest and relax as frequently as possible even when your hands are in position on the neck, and when practicing, once you have pain, you should stop and completely relax the hands and let them rest before continuing to play.
You do need to play through it, but that means rest as often as you need to. There are lots of things to do when practicing so multi-task, and do something else while resting the left hand do some finger picking patterns, right hand only, all open strings.
There are ways to be productive while allowing your hands to rest as you push them further and further.
Yet, you will experience less fatigue if you don't over squeeze the neck and don't hold unnecessary tightness in your hands. Its not a capo. Let it relax when you can.