The possible causes for armpit pain include
Swelling in the lymphatic glands in the armpit and breast area
A pull of the Pectoralis muscle which then irritates the ribs underneath.
Shaving too close to the root, or beauty products may also cause a severe allergic reaction.
As you have family history of cancer so it is very essential to rule out the underlying cancerous pathology .
As such you need to undergo a clinical examination of armpits and breast and investigations like ESR, mammogram for further evaluation.
Breast tenderness can be caused due to PMS as well.
I suggest you to consult your regular doctor for further evaluation and management.
I hope this helps.