I have a sharp pain in the lower right quadrant ofmy back. I was assuming that it was muscle but has not improved after 36 hours. Could it be kidney?

Could be. It could be related to a kidney problem if it is associated with urinary symptoms (bloody urine or burning upon urinating). If any of these above symptoms are present and you still have pain you should seek medical advice and do a urine analysis.
Maybe, somethingelse. Could be muscle, could be stone in ureter (tube from kidney to bladder), other. If abdominal component could be diverticulitis, appendicitis, inflammatory bowel disease, gyn issues. See your doc.