Yes, I think you should, especially if the member of your family is your mom or your sister. If the cancer also affected your mother's mom and or a sister of mom's, you should consider it also. Make sure that you do monthly self exams and get your yearly mammograms. A baseline mammo at 40 - with no breast cancer in the family - is very important, but if you are younger and there is direct genetic relationship with you and the person going through it, you must start sooner. Your doctor may not say it's necessary, but insist on getting it done and do it yearly - without fail. It could save your life.
I am a 15 month breast cancer survivor with virtually NO family history of breast cancer, but I got it anyway. I was fortunate in that it was caught at its earliest stage (DCIS -ductal carcinoma in situ- Stage 0), but lifelong hormone issues and my use of fertility drugs 20 years ago set the stage for me to get it. Because I was cavalier about my mammograms (foolishly thinking that since no one in my family had it I would escape scot free) I didn't get my mammo for almost two years, although ironically I was vigilant about my gynecological health and had annual exams regularly. I feared ovarian cancer due to the fertility drugs I used, which was made even more pressing when a close friend died from the disease.
I learned the hard way because of my neglect and attitude and had to go for treatment anyway. 1 lumpectomy left me slightly dented and minimally scarred, 4 weeks of radiation treatment left me burned and exhausted - the latter worsened by fibromyalgia - and a total hysterectomy (everything was removed) were the end result of that neglect and frankly, despite my luck it catching it early, I wouldn't wish that journey on anyone.
Take care of you. Please.