I would say, 'I've got period pains' or, more colloquially, 'I've got curse pains'. However, I think calling periods 'the curse' is probably something that middle-aged or older women would say - I don't really hear younger women using the expression these days.
"Premenstrual pains," literally, since "menstrual pains" occur with the period itself. PMS=premenstrual syndrome.
Edit: And they are "abdominal pains," as well, if you must say where in the body they are felt.