Can a constant pain in top breast and a little into the armpit mean breast cancer?

Breast pain: No. That is not how cancer presents itself!

Not generally: Sounds like you have a muscle, vascular, lymphatic, or fascia spasm that is an obstacle to normal movements. Find osteopathic medicine treatment (doctor of osteopathy - od that uses manual manipulation therapy, or a physical therapist trained in osteopathic manual manipulation.