Squamous Cell Carcinoma of the Lung with Superior Vena Cava (SVC) Syndrome: This diagnosis is the most likely due to the combination of symptoms such as weight loss, shortness of breath, nonproductive cough, and particularly the signs of SVC syndrome (facial swelling, facial plethora, distended neck veins, and prominent superficial veins over the chest). The patient's history of heavy smoking significantly increases the risk for lung cancer, and squamous cell carcinoma is a common type that can cause SVC syndrome due to its typical location in the central airways.

Small Cell Carcinoma of the Lung with SVC Syndrome: Similar to squamous cell carcinoma, small cell carcinoma can cause SVC syndrome, especially given its central location and aggressive nature. However, it is less common than non-small cell lung cancers like squamous cell carcinoma.
Non-Small Cell Lung Cancer (NSCLC) with SVC Syndrome: While less likely to cause SVC syndrome than squamous cell or small cell carcinoma due to its more peripheral location, NSCLC can still cause obstruction of the superior vena cava, especially if it involves the mediastinum.
Lymphoma with SVC Syndrome: Both Hodgkin's and non-Hodgkin's lymphoma can cause SVC syndrome, especially if there is significant mediastinal involvement. However, lymphoma is less common than lung cancer in a heavy smoker.

Pulmonary Embolism: Although less likely given the constellation of symptoms, pulmonary embolism can cause sudden onset of shortness of breath and can be associated with distended neck veins if it leads to right heart strain. It's crucial not to miss this diagnosis due to its high mortality rate if untreated.
Aortic Dissection: This condition can cause sudden chest pain and can lead to obstruction of the superior vena cava if the dissection involves the ascending aorta. It's a medical emergency that requires immediate diagnosis and treatment.
Thyroid Cancer with SVC Syndrome: Although rare, thyroid cancer can metastasize to the mediastinum and cause SVC syndrome. Given the facial plethora and swelling, it's essential to consider thyroid pathology, especially if there's a known history of thyroid disease.

Thymoma with SVC Syndrome: Thymomas are rare tumors originating from the epithelial cells of the thymus. They can cause SVC syndrome if they grow large enough to compress the superior vena cava.
Mediastinal Germ Cell Tumors with SVC Syndrome: These are rare tumors that can occur in the mediastinum and, if large enough, can cause SVC syndrome.
Sarcoidosis with SVC Syndrome: Sarcoidosis is a systemic granulomatous disease that can involve the mediastinum and, rarely, cause SVC syndrome if there is significant lymphadenopathy or granulomatous infiltration compressing the superior vena cava.