Musculoskeletal strain or fibromyalgia: Given the initial presentation of back pain and the subsequent development of chest pain, musculoskeletal issues are a common cause of both symptoms, especially in a young adult without other alarming features.

Costochondritis: Inflammation of the cartilage that connects the ribs to the breastbone can cause chest pain and may also refer pain to the back.
Gastroesophageal reflux disease (GERD): Can cause chest pain and, if severe, may also lead to back pain due to esophageal spasm or referred pain.
Anxiety or panic disorder: These conditions can manifest with both back and chest pain, especially if the patient is experiencing significant stress or anxiety.

Pulmonary embolism: Although less common in a young adult without risk factors, pulmonary embolism is a life-threatening condition that can cause sudden onset chest pain and, occasionally, back pain if the embolism affects the lung periphery.
Aortic dissection: A tear in the aorta's inner layer can cause severe, tearing chest pain that may radiate to the back. It's rare but critical to diagnose promptly.
Myocardial infarction: While uncommon in young females without risk factors, myocardial infarction (heart attack) can cause chest pain and, occasionally, back pain.
Pneumothorax: Air in the pleural space can cause sudden chest pain and, if large, may also cause back pain due to the pressure exerted on the thoracic spine.

Spinal tumors or metastases: Although rare, tumors in the spine can cause back pain that radiates or refers to the chest.
Osteoporotic vertebral fractures: More common in older adults or those with significant osteoporosis risk factors, but can occur in younger individuals, especially with steroid use or other secondary causes of osteoporosis.
Inflammatory arthropathies (e.g., ankylosing spondylitis): Can cause chronic back pain and, in advanced cases, may involve the chest wall, leading to chest pain.