Thanks for writing in.
By description, a golf ball sized lump in armpit region could be an enlarged axillary lymph
node. If it is not responding to antibiotics, a FNAC (fine needle aspiration cytology) test might be necessary. In this a small needle if inserted into the swelling and few cells are aspirated (sucked). This is then studied under microscope by pathologist. You have not mentioned whether it is sudden onset or present from weeks and slowly growing. If there is no pain and it has been there for long time, a chronic inflammatory condition might be present. Presence of fever
and any weight loss
is also important. You must consult a surgeon with these details.
Hope it helps.