I believe your co-worker was referring to research that claims to have found an association between deodorant use and breast cancer. It important to note that the Food and Drug Administration, the National Cancer Institute, and other large medical organizations do not support these findings. (Read more about deodorant and breast cancer.)
The bump that you have in your armpit area could be something as minor as a ingrown hair, or something more serious, like an abnormal mole. I would recommend having your doctor evaluate the bump as soon as possible. You can also view this skin cancer photo gallery to see what abnormal moles look like.