I have a sore lump under my armpit?

Lymph node. More than likely you have an acute infection somewhere on the upper extremity that is seeding a lymph node in your arm pit. The lymph node filters the bacteria, virus or fungus and then reacts as "killer cells" come to attack the agent. The lymph node responds by growing, producing more cells, and can get tender due to the agents and chemicals released. You may need antibiotics or see pcp.
Lymph node. It can be a lymph node that is inflamed. It occurs with some viral illnesses and also with bacterial ones, like cellulites that occasionally occurs in the armpits especially after shaving. There may be some inflamed sweat glands that can present as painful lumps. Finally, if you are a female, you need to have your physician check your breast to make sure there's nothing going on with it.