The armpit is called the axilla in the dog. Swelling in this area can be caused by a number of things. It could be from trauma, infection, inflammation, cancer, the presence of a foreign body, or a swollen lymph gland (from local infection or cancer). If the area is painful, or the condition worsens or persists I would recommend you contact your local veterinarian. Your vet will take a thorough history of the problem, do a full physical exam and possibly do further testing on the affected area. Tests may include a fine needle aspirate, ultrasound or xrays. A fine needle aspirate is where a syringe and needle is used to suck out a sample from the affected tissue. The sample is stained and examined under the microscope to give an idea as to the composition of the swelling.