sore breasts prior to menstruation, from what I have seen is one of the many signs of Iodine deficiency.
I know its frustrating, so many issues have same or similar side effects that it can be nearly impossible to try and figure out the cause. But keep your eye on the prize and remember finding out the true cause isnt as important as actually fixing the problem.
Often times, especially with nutrition etc, there are many times multiple contributing factors.
Stick with the basic Iodine and cosupplements to start and see how that goes and then slowly but surely tweak your plan and add items and adjust dosing a little here and a little there. Just remember it can take a while for you to actually see or feel a difference.