The most frequent type of breast lump found in a woman your age is called a fibroadenoma.  These are not dangerous, and often doctors will just leave them alone if they are certain that the lump is a fibroadenoma although sometimes the doctor will biopsy the lump just to be sure.  If it is large and causing problems, the doctor may remove the whole thing.  

Whether your risk of breast cancer is increased by your nanna's breast cancer depends on her age at time of diagnosis.  If she got breast cancer after she had menopause, her breast cancer has very little effect on your lifetime risk, and doesn't affect your risk now at all.  If she was diagnosed with breast cancer when she was in her 20's or 30's, then you may have a higher risk than the average young woman.  You would need to talk to a doctor and ask about genetic counseling to find out for sure.  

Although every now and then a woman your age does get breast cancer, it happens so infrequently that the chances that this lump is cancer are practically zero.  Even among women who are much older, the vast majority of biopsied lumps turn out to be benign (no cancer).  So keep working with your doctor to get more information about what this lump is, but don't panic or worry.  It's almost certainly nothing dangerous.