Step 1: Understanding the Concept
Each respiratory illness is named after the part it affects.
Step 2: Match the symptoms
Pneumonia is an infection of the alveoli of the lungs, which fill with fluid or pus. This causes cough, fever, chills and shortness of breath.
Step 3: Why the others fail
Sinusitis affects the sinuses, bronchitis the bronchi and laryngitis the larynx. None of them mainly inflames the lung tissue.
Final Answer:
The illness described is pneumonia.
\[ \boxed{\text{(D) }\text{Pneumonia}} \]