Armpit soreness can be a result of bacterial, fungal or viral infection. It could also be a sign of cancer. Cat scratch fever can be the culprit. Sometimes an allergic reaction to sulfur drugs can cause this soreness.
Soreness under your armpit could be one of two possible things in my mind. One of these things could be an ingrown arm hair. This causes pain and redness. The other thing it could possibly be is razerburn. Dry shaving or over shaving will cause irritaion and make them sore.