Juvenile Idiopathic Arthritis (JIA): Given the patient's age, family history of autoimmune diseases (RA, Lupus, Hashimoto's), and complaints of bilateral knee, ankle, elbow, wrist, and back pain, JIA is a strong consideration. JIA is a chronic autoimmune disease that can present with polyarticular pain and has a genetic predisposition.

Systemic Lupus Erythematosus (SLE): Although less common in adolescents, SLE can present with joint pain, and the family history of Lupus increases the likelihood. SLE is a multisystem autoimmune disease that can affect various organs.
Mixed Connective Tissue Disease (MCTD): This disease combines features of lupus, scleroderma, and rheumatoid arthritis, which could explain the patient's polyarticular pain and family history of autoimmune diseases.
Fibromyalgia: Although more common in adults, fibromyalgia can occur in adolescents and is characterized by widespread musculoskeletal pain, which aligns with the patient's complaints.

Infectious Arthritis: Bacterial, viral, or fungal infections can cause severe joint pain and must be considered, especially if there's a history of recent travel, exposure, or immune compromise.
Lymphoma or Leukemia: These malignancies can present with bone and joint pain, and although rare, they are critical to diagnose early due to their potential for severe outcomes.
Osteomyelitis or Septic Arthritis: Infections of the bone or joint can cause severe pain and have significant morbidity if not promptly treated.

Sarcoidosis: A multisystem granulomatous disease that can cause joint pain, among other symptoms, but is less common in adolescents.
Relapsing Polychondritis: A rare autoimmune disease that can cause cartilage inflammation, leading to joint pain, but is more commonly seen in adults.
Ehlers-Danlos Syndrome: A group of genetic disorders affecting connective tissue, which can lead to joint hypermobility and pain, but the presentation is usually more complex and involves skin and other systemic features.