Do a lot of people get armpit pain or is that a weird symptom?

Common. The armpit (axilla) has a lot going on in a small space...All the muscles, blood vessels, and nerves that connect the arm to the torso traverse this space, there are a lot of lymph nodes, plus there are many specialized skin glands. Axillary pain can be related to any of these structures. If there are no obvious "lumps" or areas of swelling, it is usually of musculoskeletal origin.