My daughter is older, but yes, her depression and anxiety and rage and threats (and attempts) at self-harm were much worse (dangerously so) when she was on her period. Plus, her periods were not regular at all, not even close. Even though she's in her early 20s now, we did start this birth control plan when she was a teen.
I took her to the gynecologist. That doctor reviewed everything carefully, and consulted with her other doctors. We also reviewed this plan with her psychiatrist.
All agreed that birth control could be helpful. It took 3 tries before finding the right one, so if you go this route, don't give up if one isn't helpful. My daughter ended up taking Jolessa (that's the brand name). She also takes Welbutrin and another anti-depressant, and several other medications as well.
I encourage you to be really honest with your pharmacist, and your daughter's doctors, and to consult a psychiatrist. The pharmacist is a really good ally in a situation like this.
My daughter is still not healthy by any means, but I can truthfully say that the monthly blow-ups and self-harm and anxiety attacks are much, much better after adding in the birth control.
And the pharmacist also told us that my daughter doesn't have to skip that week of "blank" pills. She takes them consistently, all the time, and every once in a while, maybe every 4 months, the gynecologist tells her to take a break for a week or so.
You'll have to prepare to communicate faithfully with the pharmacist, psychiatrist and gynecologist. Make sure the gynecologist is aware of the reason for the birth control. We've been quite clear that this has nothing to do with contraception, but with hormone control and the effects of the periods on the anxiety and other issues (my daughter is not sexually active - she's not anything active and is medically disabled and lives at home with us as her caregivers).
Also, something I learned from the gynecologist: today's birth control pills must be taken at the exact same time every single day. She explained that way back, before I had my kids (they're in their 20s now), we were just told to take a pill a day and not miss a day. But the gynecologist was extremely insistent that my daughter take the pill at precisely the same time every day. Not 10 am, and then the next day at 11:30. But every single day at whatever time my daughter chose, as long as it was every day at the same minute. My daughter sets an alarm and doesn't skip a dose, and doesn't miss the alarm. The pills are formulated differently now - I don't understand the chemistry but it really seemed important to the gynecologist, so we're not about to argue!
I hope your daughter gets the help she needs. Feel free to pm me. I understand and empathize.