Around the arm pit can contain breast
tissue, lymph nodes, as well as other tissues. I would strongly suggest seeing a doctor. It could be nothing more than a cyst, a fat or fluid filled lump. And if she's been ill it could possibly be a swollen lymph node. However, breast tissue can sometimes be found near the arm pit, so it's theoretically possible that it could be related to that.
What does the lump feel like? Is it sore at all? Does it move freely?