Will i be sick? i put on deodorant, and under one of my arm pits, it stings. i think i cut it shaving, & the deodorant says don't use on broken skin.?

You will not be sick: I am sorry that you are worried that you will be sick since this is not the case. I would stop using any anti perspirant or deodorant until the area has totally healed. You can then resume the use of it again. If you put a small amount of Vaseline over the area that was cut, it will heal a little faster

Rinse area : I doubt this will cause illness, but the skin may be irritated. Rinsing the skin with plain water will help minimize irritation

Unlikely: Assuming the use of a normal amount of deodorant, a dose received internally from a small cut would be insufficient to cause systemic illness. The warning is most likely based on the discomfort one would feel if the deodorant is applied to broken skin, not any major illness.