It is common for swollen lymph nodes in the neck and under the arm to indicate that your body is fighting off an infection or illness. If the swelling has been present for a long time or is accompanied by other symptoms, it is wise to consult a healthcare professional for further evaluation and treatment. In the case of a recent onset of swelling, it could indicate that your body is actively fighting off an infection, such as a throat infection. It is important to address any underlying infections to help reduce the swelling of the lymph nodes as quickly as possible.