Lots of people have never had an orgasm during sex, so thats probably not a problem. When you have an orgasm though everything contracts, so maybe you have a medical reason why this is hurting you...
I know you are still young but its not impossible you are about to go through the menopause, women who are, often have this during and for some time after. It might be worth thinking about if you are having anyother menopausal symptoms. Other problems that could cause this off the top of my head, maybe cystitis or some other bladder infection, or endometriosis. Not sure about these but I would think these could cause pain during sex.