ANDY'S ANSWER: Breast pain that is associated to periods is called cyclic breast pain. It normally occurs in the days just before your period. It is common and can happen at any age. It can also come and go.
What actually happens is that the higher levels of estrogen and progesterone that your body produces in the second half of your menstural cycle can cause your breast tissues to swell and become lumpy. The extra pressure can make them tender and sensitive as well as cause actual pain.
Wearing a good supporting sports bra (not an underwire kind) can help. Also taking ibuprofen or acetaminophen may relieve your pain. Some women say that caffeine makes the symptoms worse, so you could also try cutting out caffeine in the week before your period to see if that makes a difference.