This swollen lump in the armpit is a swollen lymph node. Lymphadenopathy (swollen lymph nodes) is usually caused by a viral or bacterial infection along with other numerous causes. Treatment is usually cold compresses, over the counter anti-inflammatory analgesics(pain killers) like acetaminophen or ibuprofen, antibiotics if cause of infection is suspected to be a bacteria and surgical drainage if there is any abscess formation.
I hope it helps. Take care and please do keep me posted in case you have any additional doubts. Kind regards.