Cellulitis or Soft Tissue Infection: Given the symptoms of increasing redness, swelling, and pain in the upper back, along with associated pain in the right arm, a soft tissue infection such as cellulitis is a plausible explanation. The infection could be localized to the skin and subcutaneous tissue of the upper back, potentially spreading or referring pain to the arm.

Musculoskeletal Injury or Strain: The symptoms could also be indicative of a musculoskeletal issue, such as a strain or injury to the muscles or ligaments of the upper back, which could radiate pain to the arm.
Herniated Disk or Spinal Stenosis: These spinal conditions could cause pain in the upper back that radiates to the arm, especially if there is nerve compression involved.
Costochondritis or Tietze's Syndrome: Inflammation of the cartilage that connects the ribs to the breastbone (costochondritis) or Tietze's syndrome, which affects the cartilage of the upper ribs, could cause localized pain and swelling that might be perceived as a mass.

Breast Cancer with Chest Wall Involvement: Although less likely, it is crucial not to miss breast cancer, especially if the mass is located near the breast area. Breast cancer can cause skin changes, including redness and swelling, and can invade the chest wall, causing pain.
Lymphoma: Lymphomas can present with masses and systemic symptoms. A mass in the upper back could be a lymph node involved by lymphoma, which would be critical to diagnose early.
Spinal Epidural Abscess: A serious and potentially life-threatening condition where an abscess forms in the epidural space surrounding the spinal cord. It can cause severe back pain, fever, and neurological deficits, including arm pain.
Pulmonary Embolism with Infarction: While less directly related to a back mass, pulmonary embolism can cause sudden onset of chest pain and, if associated with infarction, could potentially cause a palpable mass due to hemorrhage or inflammation in the lung tissue.

Ewing's Sarcoma or Other Primary Bone Tumors: Rare bone cancers that could present with a mass and pain in the upper back.
Multiple Myeloma: A plasma cell malignancy that can cause bone lesions, leading to pain and potentially a palpable mass.
Tuberculosis or Other Granulomatous Infections: Uncommon infections that can cause chronic inflammation and masses in various parts of the body, including the upper back.