Will a CBC test and a urine test be able to pick up on kidney problems?

Not necessarily. You need a BMP or CMP (basic metabolic panel or a comprehensive metabolic panel) to specifically test for BUN and creatinine for kidney function. If you have stones, usually a CT scan is needed but they would have shown up on a renal (kidney) ultrasound. A urine test would have shown if you were spilling blood (possibly stones), sugar (diabetes), protein (kidney problems), or if the urine pH (acidity) was low (need to increase fluid intake). Have you tried increasing your fluid intake to like 100 ounces per day? You should be drinking enough varied fluids to urinate about 2 liter per day. If you have kidney problems, it does not normally change sides like that. The kidneys are actually a lot higher than people think (toward the spine about 12 inches above the pelvic bones).