what you are describing could be something as harmless as an ingrown hair or infected or irritated hair follicle, but your armpit contains lots of lymph nodes which could also be the source of the bump. This can happen with a bacterial, viral, or fungal infections, allergic reactions (perhaps even to a new deodorant), and a number of benign conditions. It is probably not serious, but remember that there are more alarming conditions that can also cause swelling in the armpit, such as Hodgkin's or Leukemia, so just to be safe, you should probably get it checked out, especially if it doesn't go away in a few days.
Some interesting reading:
http://www.diagnose-me.com/cond/C110125.html
see a doctor any lumps should be checked.