Fat necrosis occurs if the blood supply to the fatty tissues are somehow severed or injured. Aside from the physical deformities this may cause, there is a very small chance that this can be infected and develop into an abscess. This occurrence is more common in the elderly or in patients with systemic diseases such as diabetes. However, it is very hard to tell just by the physical exam if this is indeed fat necrosis and the imaging studies such as ultrasound or mammogram may help. Women at high risk of breast cancer can undergo mammogram as early as 20 years of age, but I see no problem with you having one if your doctor deems it necessary. I suggest you discuss these options and possibilities with your doctors and I hope everything will turn out OK.
Regards and God bless.