These breast lumps are very commen in your son's age group. They are related to the changing hormones. Lymph nodes can become enlarged due to several causes ; often due to an infection somewhere in the body. If you meant swelling in the entire armpit and it's on both sides then it might well be from the cause you mentioned. It wouldn't hurt to ck. with your son's Physician for an explanation of these hormonal changes. Often these lumps will go away on their own, in time. Regards ....
Yes, it is possible it could be breast cancer. It could also be related to something else entirely.
The swelling may have indicated an allergy to the deodorant, but the lump ... there is only one. Maybe a cyst, an ingrown hair, an injury to that breast. I don't know. Swollen lymph glands point to something else. Maybe its related to puberty??
It wouldn't hurt to get this checked out by your doctor.
J