It is possible but from what you describe as your symptoms I would tend to think Fibrocystic Breast Disease. Pain is rarely associated with breast cancer but Fibroadenomas do cause pain and soreness. you definitely should have this checked out by your Physician as soon as possible. Regards .....
I am 25 and breast cancer runs in my family also, my mom had it. If you are at higher risk and you did find a lump, I would have it checked out ASAP. However, I wouldn't jump right to Fibrocystic Breast Disease. It sounds more like an infected lumph node. If you have had a child or breastfed, it is highly likely that a lymph node or a mammory duct got infected and has taken this long to be palpable and painful. I also suggest talking to your OB doc about yearly breast ultrasounds. They are not as sensitive as a mammo, but could give you peace of mind until you are old enough for mammos. Also, you can have a breast MRI: no radiation and it shows thin slices of the breast. Just something to think about.
I commend you for doing monthly breast self examination. If breast cancer runs in the family, breast cancer screening should be started 10 years earlier from the age of the first degree relative diagnosed with breast cancer. About 10% of breast cancer is hereditary. The Surveillance, Epidemiology, and End Results (SEER) data showed that the incidence of breast cancer is about 1.9% in the age group of 20 to 34 years in 2001-2005.
I agree with your decision to have the lump examined by your doctor. You may need to undergo work-ups like a breast ultrasound.