Dear NELO: A BIRAD Score of 3 indicates that the abnormality is probably a benign finding, there is less than 2% chance of cancer. Usually receives a 6 month follow-up mammogram; most level 3 abnormalities do not receive biopsy. However, given your concern, it may be worth following up with a surgeon. Your mental health is as important as your physical health. In some cases, a biopsy may be worth doing just to ease your mind.
Breasts are rarely mirror-images of each other, so it's common that a mammogram shows patterns of glands on one side that aren't identical to the pattern on the other side. That's what asymmetrical tissue means, and it's by far most often not significant. One of the ways to help is to get additional views, with compression. When you squeeze tissue away, if there's cancer there it typically become more prominent; so when compression makes the area less noticeable it is strong evidence that it's merely asymmetry as opposed to something significant. What to do in those situations depends on many things, not the least of which is the patient's desires. Given your family history and concerns, it's understandable that you are very worried and less comfortable with a 6 month checkup (which is a common recommendation). So you ought to talk it over with your doctor, or get another opinion, possibly from a surgeon. Whereas it sounds like it's ok, if waiting will drive you crazy, it's reasonable to consider biopsy for peace of mind.