This is what I've found about lymphatic drainage of the upper limbs.
https://teachmeanatomy.info/upper-limb/vessels/lymphatics/Practically all superficial and deep lymphatic vessels drain to the lymph nodes in the axilla (armpit) .
If you think that lymph fluid flows in one single direction towards the nodes and from there to the bigger lymphatic ducts, which have valves to prevent back flow of fluid, that would mean estradiol coming from the arms couldn't reach the breasts via axillary nodes, BUT that's not the case, because 'Valves are found in larger lymph vessels and collecting vessels and are absent in the lymphatic capillaries.'
https://med.libretexts.org/Bookshelves/Anatomy_and_Physiology/Book%3A_Anatomy_and_Physiology_(Boundless)/19%3A_Lymphatic_System/19.2%3A_Lymphatic_Vessels/19.2A%3A_Lymphatic_Vessel_StructureSo, in theory, estradiol inside upper limb lymphatic capillaries could reach the breasts via back flow from axillary nodes, BUT lymph nodes afferent vessels (that directs lymph into the node) have a valve to prevent back flow, so, in practice, estradiol couldn't reach the breasts, unless there's infection or inflammation going on which could cause swelling of the nodes and disturb the dynamics of lymph flow.