Unfortunately, some boils or abscess do not surface and break, but the infection can spread inwards. This can become quite serious and turn into a fistula.
I would not recommend anyone lancing their own boils or abscesses. This is the decision that the doctor would make and do if he deemed it necessary.
Applying a drawing ointment is not the same as lancing, but would help to draw the rubbish to the surface.
A doctor's visit is recommend.
I agree with the other comments. It probably is a staph infection. a hot compress or ointment may help. But since it is under your arm I would see a doctor as there are lymph nodes under the arm and if it breaks open it may spread the infection. Best to err on the side of caution here. I wouldn't lance it because it is in the area of the lymph nodes and I would see the doctor first. They can decide whether or not to lance it. I think it is better not to and to get the antibiotics from the doctor and have it go down on its own. If you see any red streaks in the area or you develop a high fever go to the ER.
mkh9
If the skin is not broken you could apply some drawing ointment that you can purchase from the pharmacist.
As it is hurting a lot, I would suggest a check up with the doctor. Sometimes these are boils or an abcess forming.
If you doctor feels it is required, he may prescribe an antibiotic for the infection and may also need to lance the bump if it is ready but a head is not forming.
The bacteria can travel into the body, so do not neglect it.
Best wishes.
I get boils also, it will come out better if you put hot wash cloth on it. It comes from something rubbing on your skin and heat. Got one once from wire in my bra. If it continues and you are worried, go to the doctors. Try hot cloths.