re: Should I change the way I grip my pistol?

Dominant thumb over non-dominant thumb with thumbs along the frame pointing at your target.

Referred to as a "thumbs forward" grip. It gives you more control of the handgun closer to the muzzle and provides much better recoil management.

Refer to my video or this picture:

Handgun Accuracy and Proper Technique



Notice how his left thumb extends in front of the trigger guard. This gives you much more control near the muzzle.