The surgical procedure involved is Modified Radical Mastectomy (MRM), which includes axillary lymph node dissection. Removal of axillary lymph nodes disrupts the lymphatic channels draining the upper extremity, leading to accumulation of protein-rich lymph fluid in the interstitial tissues -- clinically manifest as arm swelling (lymphedema). Post-mastectomy lymphedema is the most common cause of upper limb swelling in this setting, with an incidence of $2-10\%$. Key contributing factors include: extent of lymph node dissection, adjuvant radiation to the axilla, and post-operative infections. Angiosarcoma (Stewart-Treves syndrome) is a rare malignant transformation arising in chronic lymphedema, not the primary cause of swelling. Recurrence or metastasis may obstruct lymphatics but is not the most probable explanation in the immediate post-operative context. \[\boxed{\text{Upper limb Lymphedema}}\]