What can be the causes of pain in breasts? can their growing also be a cause of pain?

Yes: Pain is a signal generated by irritated end nerve fibers that are all over our skin including that of the breasts. When breast tissue volume increases either due to natural overgrowth or hormonal stimulation (like premenstrual), they stretch the overlying skin and thus you feel tenderness or mild pain. This should not last long and not be associated with warmth or fever (signs of inflammation)