How could I know if the lumps are just fibricystic breast changes or something more serious like breast cancer?

Biopsy. A simple biopsy would give you your answer if the lesions are suspicious on imaging.
See your doctor. I have been a breast cancer surgeon for almost 20 years and I am still fooled by some exams. With that said, there are some generalizations about which breast lumps are more concerning than others. Cancers tend to be rock-hard, fixed, and 3-dimensionally round or oval. Benign lumps tend to be rubbery, cigar-shaped or pancake-shaped.
See a doctor. Have a physical examination with your doctor, mammogram, and a breast ultrasound if indicated. If there is anything needing further evaluation after that, then MRI or breast needle biopsy may be indicated next.