Numbness in the underarm area can be caused by pinched nerves in the neck. It is normally accompanied with conditions such as underarm numbness, discomfort and sensitivity to cold. This disease is often caused by degenerative disc disease on bone spurs. An MRI of the neck would reveal your condition further. I would suggest you to consult your doctor and conduct appropriate tests like MRI, Electromyography, Nerve condition study etc for proper diagnosis.