You should definitely be evaluated by your doctor
Exactly as you say in your question, it is a completely reasonable possibility that you have a swollen lymph node in your armpit (or axilla). The natural question, though, is why that lymph node is swollen.
A couple of potential causes of enlarged lymph nodes include infection/inflammation further out along the affected limb (distally), breast cancer (as you ask), or even a cancer of the lymph node itself (lymphoma
). As you surely realize, a complete history and physical examination with your doctor will help tease apart the possible causes, and figure out which is most likely.
While there are less concerning causes in addition to those I list above, you really ought to be evaluated to rule them out. A skin or soft tissue infection of the right arm could require antibiotic treatment, and depending on the history surrounding this lump, simple blood and/or imaging tests could be necessary to exclude some of the more dangerous conditions.
While breast cancer would be rather unusual in your age group, there are lymphomas that are more common in younger people. It is not necessarily statistically likely that you have a dangerous condition, but it is definitely worth seeing your doctor. Together, you should be able to establish a reasonable diagnostic plan.