what you describe could be several things, although cancer is not likely to be one of them, because of the coming and going. It could be ectopic breast tissue (breast tissue that's away from the breast itself). Under the arm is a common location; and it can get larger and painful with hormone cycles. Some infections, such as in sweat glands or hair follicles can behave that way, too. It sounds like something that needs to be seen and evaluated; but it's not likely to be anything very dangerous.
Dear AUNTM001: Because these "lumps" come and go, it is unlikely that they are related to cancer. Also, because they are painful, and seem to occur with your cycle, they may be cystic in nature. If you are really concerned, the lumps grow and do not go away, or if the pain is unbearable, you may wish to see a doctor sooner.