Pneumonia: This is often the first consideration due to its high prevalence and the direct link between infection, inflammation, and the symptoms presented. Pneumonia can cause both shortness of breath due to inflammation and fluid filling the airspaces, and coughing up blood (hemoptysis) due to the erosion of blood vessels within the inflamed lung tissue.

Chronic Obstructive Pulmonary Disease (COPD) Exacerbation: Patients with COPD can experience worsening of symptoms, including shortness of breath and, less commonly, hemoptysis, especially if there's a significant increase in airway inflammation or infection.
Pulmonary Embolism: While more commonly associated with sudden onset shortness of breath, pulmonary embolism can also cause hemoptysis, especially if there's infarction of lung tissue.
Bronchitis: Both acute and chronic bronchitis can lead to coughing up blood, especially if there's a significant inflammatory component or if the airways are chronically irritated.
Lung Cancer: This is a critical diagnosis to consider, especially in smokers or those with a significant smoking history, as lung cancer can cause both obstructive symptoms leading to shortness of breath and hemoptysis due to tumor erosion into airways or blood vessels.

Tuberculosis (TB): Although less common in some regions, TB is a critical diagnosis not to miss due to its public health implications and the need for specific treatment. It can cause both shortness of breath and hemoptysis.
Pulmonary Arteriovenous Malformation: These rare anomalies can cause hemoptysis due to the abnormal connection between arteries and veins in the lung, which can rupture and bleed.
Goodpasture Syndrome: An autoimmune disease that can cause both renal failure and pulmonary hemorrhage, presenting with hemoptysis and shortness of breath.
Mitral Stenosis: A cardiac condition that can lead to pulmonary congestion and, in severe cases, hemoptysis due to the rupture of small vessels in the lung.

Wegener's Granulomatosis (Granulomatosis with Polyangiitis): A form of vasculitis that affects small- and medium-sized vessels and can cause a wide range of symptoms, including hemoptysis and shortness of breath.
Lymphangitic Carcinomatosis: Metastatic cancer that spreads to the lymphatic vessels of the lung, causing shortness of breath and potentially hemoptysis.
Pulmonary Alveolar Proteinosis: A rare condition characterized by the accumulation of surfactant-like protein and phospholipids in the alveoli, leading to respiratory failure and potentially hemoptysis.
Idiopathic Pulmonary Hemosiderosis: A rare condition of recurrent diffuse alveolar hemorrhage, leading to hemoptysis and shortness of breath, without an identifiable cause.