Grip strength: does it ever get better? 😕

My hands are killing me whenever I go heavier than 35 pounds per dumbbell for squats and deadlifts. I find it hard to do 3x8 (my hands just want to hide and die in peace) but feel like it's not overly challenging for my legs.

Does grip strength ever catch up? I feel like I've been at this level for ages .

What has been your experience?