M.R.
Have you tried hand-expressing or using a pump? That might or might not work, but it certainly is worth a shot.
I'm so sorry to hear about your family history of cancer. In this case, you may wish to schedule an appointment with either your ob-gyn or your primary doctor. Either one can do an exam and, if necessary, send you to a specialist.
It's awesome that you are well-aware of your 'breast health' and are able to give attention to this issue immediately. While this may not be a cancerous lump, it's worth getting checked out. Good for you for being so proactive with this - it can make a world of difference if there is a problem.