Musculoskeletal Pain: Given the patient's age and history of asthma without other cardiac history, musculoskeletal pain is a common cause of chest pain that radiates to the arm, often related to strain or overuse.

Costochondritis: Inflammation of the cartilage that connects the ribs to the breastbone, which can cause sharp pains in the chest that may radiate to the arm.
Precordial Catch Syndrome: A condition that causes sudden, sharp chest pain, often radiating to the arm, due to irritation of the nerves in the chest wall.
Gastroesophageal Reflux Disease (GERD): Can cause chest pain that may radiate to the arm, especially after eating or at night, due to stomach acid flowing back into the esophagus.

Acute Coronary Syndrome (ACS): Although less likely in a young patient without cardiac history, ACS (including myocardial infarction) is a critical diagnosis that must not be missed due to its high mortality rate. The equal blood pressure between arms makes aortic dissection less likely but does not rule out ACS.
Pulmonary Embolism (PE): Can cause chest pain that worsens with deep breathing and may radiate to the arm, with a history of asthma potentially increasing the risk of PE due to chronic respiratory issues.
Aortic Dissection: Less likely given the equal blood pressures between arms, but this condition is so critical that it must always be considered in the differential diagnosis for chest pain.

Pneumothorax: Although more common in patients with a history of lung disease like asthma, pneumothorax (collapsed lung) is a rare cause of chest pain that can radiate to the arm, often accompanied by shortness of breath.
Pericarditis: Inflammation of the sac surrounding the heart, which can cause chest pain that may improve with leaning forward and can radiate to the arm.
Esophageal Spasm or Rupture: Rare conditions that can cause severe chest pain radiating to the arm, often associated with difficulty swallowing or severe epigastric pain.