I'm so sorry, I can't find much on testosterone and fibrocystic breasts, and I bet you couldn't either, which is why you're asking.
You can look at this 2 ways - either no research has been done on this at all, or it's not a concern with testosterone. Since birth control pills can help this, and they lower the cycle-related hormone levels, it would seem that testosterone may help, but I can't find anything at all to back that up.
It might be worthwhile to see a breast specialist first, especially since it worsens your dysphoria every month. I'd hate for it to make things worse. :(
Please let us know what you find out, and I'm sorry I couldn't find anything to help.