Best advice from MK...don't worry until you know you have something to worry about. I, too, had a strong family history of cancer (reads something like yours,actually). I had a long history of cysts, but I could feel a big difference between the cysts that I had dealt with for years and the cancerous lumps that I later had. Based on family history, your doctor probably just wants to make sure that cysts are all that you have.
Based on my family history, I decided to have genetic testing done, and to my surprise, and that of the geneticists, too, I think, I was negative for a known genetic predisposition.
I hope your visit with the surgeon goes well. He may be able to aspirate the cysts, but he may want biopsies as well, just to be sure.
Best of luck at your appointment tomorrow. Let us know how it goes.