(Female here.) The hormones involved in PMS can affect just about any female. Being an INTJ doesn't mean you'll never experience strong emotion, or act on it; it merely describes that your primary mode is more emotionally detached.
Hell, I'm a pretty cold-hearted INTJ, but I get hyper-emotional even more often than once a month because of my bipolar cycles. I almost never get weepy over empathising with others' feelings, which I figure for me is part of being an INTJ, but even if you get emotional in that sense, it's not difficult to explain in the context of a PMS cycle.
Basically: INTJ doesn't say you can't be influenced by emotions. It just says that when you experience them, most of the time you probably won't prefer to base your actions on how you feel over what you think.
As someone who hates being dictated by irrational emotions, I've just learned to recognise when my upsets are part of such a biological cycle, and not dwell on them if I can avoid it. I'm on the pill more recently, which does a remarkable job of minimising my period symptoms including weepiness and crankiness, but I still get crying spells in the middle of my depressive episodes. And when I'm hit by them, I just try to relax and ride them out. If you can remember and appreciate that feeling down doesn't mean that things are any worse than usual, and that you'll be feeling better soon, you'll probably find it easier to get through. That's what works for me.
If you haven't already, though, and your emotional problems are getting in the way of day-to-day life, you should probably consider talking to a counsellor and/or seeking diagnosis and any appropriate treatment for depression or whatever it might be that's troubling you. If you're not on the pill, I suggest talking to a doctor about it, because you might find it helps the mood swings, or at least relieves the physical symptoms enough to not stress you out so much.