In these cases it may not be felt as a lump but show up on mammogram or ultrasound. There are side effects to any medication. That is why it is only given to women at sufficiently high risk to justify use. This is not a problem for a woman who has had a hysterectomy. There are other side effects, including a slight increase in the tendency to form clots in the veins.
Tamoxifen does decrease the risk of a second cancer developing in the other breast.
Actually it was through this observation that physicians recognized it might decrease the risk of breast cancer for other women. There was a study in which women received Tamoxifen after treatment for breast cancer. Those women had substantially fewer new cancers develop in the opposite breast. I don't have statistics that I can quote, but every physician who takes care of women with breast cancer has seen numerous cases where a mammogram was normal but the woman had breast cancer. This is why we insist on both mammography and physical examination.