Whenever I lay down after I drink some water (any amount), my lower back (possibly around my kidneys) begins to hurt. It's just very uncomfortable.

Drink water. There is no way that water drinking can be involved in back pain. A hiatal hernia hurts under the rib cage. Sx are from you spine or rarely Renal. Check w/ Murphy punch striking kidney area with the pinky side of your fist. A light tap is painful with kidney problems. Otherwise get a thoracolumbar x-ray for old injury or congenital problems. IV shooters get a disc infection.