20yr/old female. Hardened lower right abdomen with lump, causing mild pain, tender when palpated. Not appendix or colon, no injury. What could it be?

Exam needed. An examination will be needed to determine the cause of the lump and the pain. Ovarian cysts are common, but a doctor visit is warranted to make a diagnosis.
Abdominal mass. The mass could be from the abdominal wall in which case it will stick out when you raise your head (as in doing crunches) while lying on your back. An ovarian mass is another possibility. Ultrasound or CT scan should delineate these possibilities.