Costochondritis: This condition, also known as chest wall pain syndrome, is characterized by sharp pains or aches in the chest, typically on the left side. The pain can be exacerbated by exercise, deep breathing, or movement, and is often described as stabbing. Given the nature of the pain described (stabbing, increases with high heart rate), costochondritis is a plausible explanation.

Musculoskeletal Strain: The chest wall is composed of muscles, bones, and cartilage. High-intensity exercise can lead to strain or injury of these structures, resulting in pain that is localized to the left side of the chest and worsens with increased physical exertion.
Exercise-Induced Bronchospasm (EIB): Although more commonly associated with asthma-like symptoms, EIB can cause chest tightness or pain, especially during intense exercise. The pain might not radiate and could be perceived as stabbing, especially if the bronchospasm is severe.
Gastroesophageal Reflux Disease (GERD): GERD can cause chest pain that is often described as burning but can also be sharp or stabbing. Exercise, especially high-intensity exercise, can exacerbate GERD symptoms by increasing intra-abdominal pressure, thus potentially causing or worsening chest pain.

Acute Coronary Syndrome (ACS): Although less common in younger individuals, ACS (including myocardial infarction) must be considered, especially if risk factors are present. The pain of ACS can be atypical, especially in women, and might not always radiate or present with the classic symptoms of pressure or heaviness.
Pulmonary Embolism (PE): PE can cause sudden onset of chest pain that worsens with deep breathing or exertion. The pain can be sharp or stabbing and is a medical emergency.
Aortic Dissection: This is a rare but life-threatening condition where there is a tear in the aorta's inner layer. The pain is often severe, sharp, and can be localized to one side of the chest. It is crucial to consider this diagnosis, especially in patients with risk factors such as hypertension or aortic aneurysm.

Pneumothorax: A spontaneous pneumothorax can cause sudden, sharp chest pain that worsens with deep breathing or movement. It is more common in tall, thin males but should be considered in anyone with sudden onset of chest pain.
Pericarditis: Inflammation of the pericardium can cause sharp, stabbing chest pain that can improve with sitting up and leaning forward. It is less common but should be considered, especially if accompanied by a fever or recent viral illness.
Mitral Valve Prolapse: This condition can cause chest pain, often described as sharp or stabbing, which may be related to mitral valve dysfunction or associated with anxiety and panic disorders. It is a less common cause of chest pain during exercise.