Can you have ovary pain during menstruation? meaning the pain is not centered in the lower abdomen but to the side (right in my case) similar to ovulation pain. comes in seconds long waves of twinges. thanks?

I know it is possible to feel pain in other places apart from the organ because of innervation and what we call referred pain. This is because both organs have the same nerve root and the pain in one organ may appear as if it is coming from the other organ. It does not sound like a bad pain that you have, and you know that Ibuprofen helps menstrual pain.

Menstrual pain, or dysmennorha, may indicate pelvic disease. There are methods to control the pain if severe. It sounds like a visit to a trusted ob-gyn is in order.