Do swollen lymph nodes all over the body mean that it is not breast disease?

Breast cancer can lead to systemic disease. Cancer cells can invade the ipsilateral axillary lymph nodes via the lymphatic vessels at the lateral border of the pectoralis major muscle, then the subclavian lymph nodes to the supraclavicular lymph nodes, and then the venous blood stream via the thoracic duct (left) or right lymphatic vessels to metastasize to distant areas.
The cancer cells may also drain into the parasternal lymph nodes via the medial lymphatics and along the intercostal branches of the internal mammary lymphatics. In addition, early breast cancer can be metastatic in the bloodstream, and cancer cells can invade the bloodstream directly and lead to distant metastases, resulting in multi-organ metastases.