Chronic Obstructive Pulmonary Disease (COPD) Exacerbation: Given the patient's 50-year pack history of smoking and symptoms of shortness of breath (SOB) and intermittent chest pain (CP), a COPD exacerbation is highly plausible. The negative low-dose computed tomography (LDCT) scan last year reduces the likelihood of lung cancer being the primary cause of her current symptoms, but does not rule out other complications related to COPD.

Pneumonia: The presence of hemoptysis, SOB, and CP could indicate pneumonia, especially in an elderly patient with a history of smoking. The elevated A1C suggests poorly controlled diabetes, which increases the risk of infections, including pneumonia.
Pulmonary Embolism (PE): Although less likely given the absence of specific risk factors mentioned (e.g., recent immobilization, surgery), PE cannot be ruled out without further testing, especially in a patient presenting with SOB and CP.
Acute Coronary Syndrome (ACS): The patient's symptoms of CP and SOB could also suggest ACS, particularly in the context of her age and potential for cardiovascular disease.

Lung Cancer: Despite the negative LDCT scan last year, lung cancer must be considered, especially with hemoptysis and a significant smoking history. Rapidly growing tumors or those in areas not well-visualized on the previous scan could still be present.
Tuberculosis (TB): Hemoptysis is a classic symptom of TB, and although less common in this demographic without specific risk factors, it is a diagnosis that could have severe consequences if missed.
Aortic Dissection: This is a life-threatening condition that can present with CP and SOB. Although it is less likely without specific risk factors (e.g., hypertension, known aortic disease), it must be considered in the differential due to its high mortality if not promptly diagnosed and treated.

Mitral Stenosis: This condition can lead to hemoptysis due to pulmonary congestion and could be considered in the context of CP and SOB, although it would be less likely without prior evidence of valvular disease.
Goodpasture Syndrome: An autoimmune disease that can cause hemoptysis and renal failure, it is rare but should be considered in patients with unexplained hemoptysis, especially if renal function is impaired.
Wegener's Granulomatosis (Granulomatosis with Polyangiitis): A rare autoimmune disorder that can cause hemoptysis among other symptoms. It would be an unusual diagnosis but should be considered if other causes are ruled out and there are suggestive findings on imaging or laboratory tests.