NSAIDS are non-addictive.
Taking a few for one, maybe two days of a period isn’t going to adversely effect the vast majority of people.
I really think you have no clue about how severe period pains and dysmenorrhea can be. It isn’t some little twinge in your abdominal region that you can deal with or overcome with exercise. For the last few years my periods on the whole have been a bit painful but nothing that has stopped me going to work or functioning normally, most months I have no need for ibuprofen any more. If this is how yours have always been, you are very lucky and you have no idea how bad it can get.
If you did your reading, you would know that cramps are caused by uterine contractions to expel the lining. In most women, these are mild contractions for some dysmenorrhea sufferers they can be worse that *typical *childbirth contractions.
When they were really bad, I could actually time the length of a cramp and the time between them.