Do long lasting swollen lymph nodes in the armpit most likely mean breast cancer?

No. There are many reasons to have swollen lymph nodes. Some are common problems, like infection other are cancerous. Breast cancer is not the only cancer to cause lymph node enlargement. This can only be answered with an examination by a doctor.
When it comes. To cancer, only looking at cells under the microscope can provide reliable answers. You need a physical exam of your brest and axilla, a mammogram and then a biopsy.

Related Questions

I have 2 peasize swollen lymph nodes been under armpit for 6 months. No pain/itch. I'm 24 and not married, would there be a chance for breast cancer?

Small chance. It would be a good idea to be evaluated by your family doctor or surgeon. Most lymphadenopathy in young people is related to reactive benign cause like infection, tattoos, dermatitis, or medications like dilantin. Breast cancer is rare at your age, but not unheard of especially if there is a family history. Hodgkin lymphoma is also a consideration in young women.
Unlikely at your age. Your entire axillary area you will have 20 times more lymph glands than 2, any inflammation in upper arm chest, breast will result in enlarged lymph nodes besides tumors, pea size is not big, in thin people they can be feel normally, don't worry, go and see your doctor.

Swelling of lymph nodes under the arm is a symptom of breast cancer? Are the swollen lymph nodes supposed to be pain-free?

Can be. Usually a breast mass would be felt by the time breast cancer has spread to enlarged lymph nodes that can be felt under the arm. Usually the lymph nodes are painless. Any physical change you are feeling should be evaluated with a doctor and likely a mammogram. Many things including infections and cancers can cause enlarged lymph nodes.
No neccasarily. Lymphatic system absorbs/carries things too big to go into the arteries/veins like bacteria eaten by white cells and digested food. Lymph nodes "taste" the lymph for anything bad like bacteria/viruses/cancers, etc. When it detects a problem, it alerts the immune system and your body reacts. They enlarge in response to the inflammation they create when they react. They shrink when all is well.

Could a swollen lymph node be breast cancer?

Possibly. A swollen lymph node in the armpit could be from breast cancer but in most patients, it is much more likely to be a benign swelling from a number of other causes. Regardless, you should have your doctor check it out.
Could be many things. Swollen lymph node in the arm pit can be caused by various things like reactive process to infection, trauma, inflammation, etc- including malignancy- could be breast, lymphoma etc. Infection is the most common thing that give you swollen lymph node. To be sure, however, go to see your doc and have yourself checked carefully. Good luck.