Lower right side abdomen pain, hurts when lifting up leg 1 night ago, today pain is gone but it feels sored lower r. side abdomen and back. why?

Hard to say, but....: It's hard to diagnose on the internet, but if this pain gets worse again, especially if it comes with a loss of appetite and nausea, you need to see a doctor or urgent care right away. Lower right side pain with leg lift + nausea + loss of appetite make drs. Worry about your appendix. Without the nausea/loss of appetite it sounds like you pulled a muscle in your lower back/core.

See internist: It is not uncommon for appendicitis on the lower right hand side of your abdomen to irritate the psoas muscle which is used to help lift your leg. Any inflammation in this area could cause your symptoms and you may benefit from imaging such as a ct scan to evaluate possible pathology in this region.