I don't recall having any nightmares about it, but I am guessing it's because you know roughly when you're going to be getting it. I have this little period tracker app on my phone, but I never look at it unless I think I am late (which is usual).
I'd try putting up a dreamcatcher, they're supposed to catch nightmares; we have a few in the house and I never have bad dreams. Or... if you're not into the Native thing, the nightmares might stop if you can try to calm yourself and face your fears before going to bed. Try to relax in whatever way works best for you, whether it's drinking some herbal tea or killing a punching bag, and just keep telling yourself that it's okay, the red death is going to come eventually but you'll survive because you're a tough man. From what I've heard, dreams are supposed to be your subconscious trying to tell you something, so if you face it during the day and try to sort it all out, it shouldn't have to come out in your dreams.
And there are ways to throw your schedule out of whack, like drastic changes in diet can do it for some people, lots of exercise, etc. It can be dangerous to try to mess it all up though, so just be safe.