I have understood your concern and it is absolutely valid. Blood discharge through the nipples warns us about cancer of the breast. You have not mentioned your age. It also plays a great role.
Your family history of cancer breast is definitely worrying concern with blood through the nipples and demands a thorough check up for the same.
Do you feel any tumour or limp in your breast? Please try to feel it. Remember, do not feel the breast between the fingers, feel it by the flat of the hand. If there is any tumour, whether it moves? The cancer tumour never moves.
Usually the cancer tumour does not pain. But that cannot be the criterion for ruling out cancer breast.
Is the skin of your breast looking like orange skin anywhere? It so happens in cancer of breast.
Is the nipple drawn in? It so happens in cancer breast.
However, you have undergone mammography which has reported as no cancer. This is a good sign. Still, I would advise you to complete all the investigations your doctor has advised you for detection of for cancer breast.
Even if you are diagnosed not to have cancer breast, you should get your work up done every year considering your family history. Also, please go on carrying out your self palpation of breast frequently. You can find good guidelines with illustrations of the same on net.
Remember, cancer is not the only disease which gives rise to blood through the nipples. Some non-cancerous tumours or infections also can do that. The very fact your breast is tender suggests that there is mostly some infection. Could be infected breast tissue or some tumour in the breast - even cancerous also - which has got infected. This can be tackled by antibiotics which if needed, your doctor will prescribe you.
However, do not presume this as a non-cancerous lesion unless the cancer has been ruled out completely by whatever investigations required.
I hope I have clarified your doubts. If any thing is needed, you may ask me.