**Core Concept**
Sarcoidosis is a systemic granulomatous disease characterized by the formation of non-caseating granulomas in various organs, including the lungs. The presentation of bilateral hilar adenopathy with or without pulmonary infiltrates is a classic radiographic finding.

**Why the Correct Answer is Right**
The patient's symptoms and radiographic findings are consistent with pulmonary sarcoidosis. The presence of eggshell calcifications in hilar adenopathy is a hallmark of chronic sarcoidosis. The formation of non-caseating granulomas leads to inflammation and scarring in the lungs, resulting in symptoms such as shortness of breath and cough. The granulomas can also lead to the formation of calcified lymph nodes, which are visible on chest x-ray.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because the patient's presentation does not suggest a primary infectious process, such as tuberculosis or fungal infection, which would more likely present with cavitations or upper lobe predominance.
* **Option B:** This option is incorrect because the patient's symptoms and radiographic findings do not suggest a primary malignant process, such as lung cancer, which would more likely present with a solitary pulmonary nodule or mass.
* **Option C:** This option is incorrect because the patient's presentation does not suggest a primary autoimmune process, such as rheumatoid arthritis or lupus, which would more likely present with systemic symptoms and multiple organ involvement.

**Clinical Pearl / High-Yield Fact**
Sarcoidosis can present with a wide range of symptoms, including pulmonary, cardiac, and skin manifestations. The disease can be asymptomatic, and the diagnosis is often made incidentally on chest x-ray.

**Correct Answer:** D. Sarcoidosis.