I am having random sharp pains in my abdomen. Mainly between my right lumbar area and inguinal. And it doesn't feel like menstrual cramps.?

A number of things. That is a common location for pain from kidney infections or kidney stones. In addition any pelvic pathology like an ovarian cyst could present in that location. It is also possible you just have a strained muscle and keep reinjuring it because it is difficult to rest those muscles.
Numerous causes. A better history is needed to help with diagnosis. This could range from gynecological problems to a. Kidney stone or gallbladder issues. This kind of pain would be best served by a history and exam by a physican. An urinalysis, blood work and imaging such as a vaginal and right upper quadrant ultrasound may be needed to make the diagnosis.