Your nipples could be aggravated by exposure to irritants including , soap, detergents,lotions and maybe also wearing a new bras which could be irritating your skin.Hormonal changes in your body during puberty could also be causing the itchiness.
It is very difficult to give you a precise answer concerning your problem.Your symptoms though are NOT a sign of breast cancer particularly because it's happening on both your nipples and also because at your age that would be something very rare indeed.
Some deodorants, that could clog pores, or shaving the armpits, could cause an infection of the hair follicles causing the lump you are describing.
For exact diagnosis,I would urge you to consult your doctor/dermatologist for a breast exam so that these skin problems you are having can be treated successfully.
Take care and God Bless..
Thanks for this post, really informative. helped me understand the breast cancer symptoms thanks zouzi for your answer !!!