Pulmonary Embolism (PE): This is the most likely diagnosis given the acute onset of shortness of breath following weeks of leg pain, which could be indicative of deep vein thrombosis (DVT). The combination of these symptoms, especially in the context of hemodynamic instability, strongly suggests a pulmonary embolism.

Deep Vein Thrombosis (DVT) with impending PE: While DVT itself might not directly cause shortness of breath, the concern is that it could lead to a PE, which would explain the respiratory symptoms.
Cellulitis or sepsis from a leg infection: An infection in the leg could lead to sepsis, which might cause shortness of breath due to the systemic inflammatory response. However, this would typically be accompanied by other signs of infection such as fever and localized redness.
Cardiac conditions (e.g., myocarditis, pericarditis): These could cause shortness of breath and might be associated with leg pain if there's an embolic event or if the cardiac condition leads to decreased mobility and subsequent DVT.

Aortic dissection: Although less common, an aortic dissection could present with acute shortness of breath and leg pain due to involvement of the aorta and its branches. It's a medical emergency that requires immediate attention.
Cardiac tamponade: This condition, characterized by fluid accumulation in the pericardial sac, can lead to hemodynamic instability and shortness of breath. It might be considered if there's a history of trauma or if other signs such as muffled heart sounds are present.
Severe asthma or COPD exacerbation: While these conditions primarily affect the lungs, they can cause significant shortness of breath and, in severe cases, lead to hemodynamic instability.

Fat embolism syndrome: This is a rare condition that typically occurs after a major trauma, especially fractures of the long bones. It could present with respiratory symptoms, among others.
Venous air embolism: Although rare, this could occur in specific contexts (e.g., medical procedures, trauma) and would require immediate intervention.
Thromboangiitis obliterans (Buerger's disease): A rare disease of the blood vessels that could potentially lead to both leg pain and respiratory symptoms if there's significant vascular involvement, though this would be an uncommon presentation.