Birth control that stops periods???

So I have a very, VERY, bad period, one that's super long, heavy, with intense cramps that keeps me from eating and/or makes me throw up, and gives me migraines which make me dizzy and once almost made me pass out. I started a birth control called Trinessa to help regulate it and at first it seemed to work fine, but my last period was one of the worst ones in my life. I still want to have kids in the future, so getting a procedure done is out of the question. I'm also taking anti anxiety meds, I don't know if that changes the way the birth control works but it's worth mentioning. I'm just really tired of living in this hell and really need some help. Any of you ladies know a birth control that could help me? My bad periods come genetically, all the women in my family on both sides had terrible periods. Sorry for the long post, just really need some insight.