Hello~I would tell your doctor as soon as possible, any new bleeding needs to be thoroughly checked, especially since cancer runs in your family.
Hi. Sometimes we get hormonal bleeding when we shift our hormones. That is probably the case for you. Abnormal bleeding that women talk about for cancer is more related to say after menopause you still bleed or heavy bleeding with your cycle that would mean your lining is thicker than it should be. It makes sense that you have some break through bleeding at the time of getting the depo again. I would talk to your doctor. They will probably tell you to take an NSAID like ibuprofen which can stop the bleeding or they may add some estrogen, both of which are used to combat depo shot bleeding. Here's an article to look at too. https://www.healthline.com/health/birth-control/depo-shot-bleeding-how-to-stop-it
Let us know how you are doing and what you think!