A sore red bump under the armpit is a common symptom of an ingrown hair, a condition that occurs when hairs curl around and grow backwards into the skin, according to WebMD. Ingrown hairs can also grow sideways in hair follicles that have become clogged with dead skin.
In certain cases, ingrown hairs resolve on their own within a few days' time; however, ingrown hairs that become infected may require antibiotic treatment, according to HowStuffWorks. Soaking the affected area in warm water may help to soften the burrowed hair and make it easier to remove with a sterilized needle. Careful removal of ingrown hairs is essential to prevent additional infection and skin irritation.