What can make your breast hurt and it leads to your under arm?

Several things . Breasts can hurt around ones period. Mastitis can hurt but a doctor can see redness and feel excess warmth. If one sees nothing need to examine for any masses and with any suspicious finding obtain mammogram based on your age.
Fibrocystic tissue. Fibrocystic breast disease is the most common reason for beast tenderness and pain. Caffeine (coffee, soda, tea, chocolate) will cause that tissue to retain fluid and increase the tenderness. Since over half of the mammary tissue in the breast is in the upper outer quadrant of each breast and that extends well up under the arm into the armpit - there is usually more discomfort in that area.