Acute Bronchitis: This condition often starts with a dry cough that may later produce yellow sputum. The presence of mild fever and body aches, such as pain in the legs and back, are common accompanying symptoms. Acute bronchitis is typically caused by a viral infection, which aligns with the described symptoms.

Influenza (Flu): Characterized by sudden onset of high fever, chills, dry cough, and muscle pains, including back and leg pain. The flu can lead to secondary bacterial infections, which might explain the yellow sputum.
Pneumonia: Although it can present with more severe symptoms, mild cases of pneumonia, especially in the early stages, might manifest with mild fever, dry cough that becomes productive, and body aches.
Musculoskeletal Strain: The back and leg pain could be due to a musculoskeletal issue, with the cough and mild fever being coincidental or related to a minor viral illness.

Pulmonary Embolism: Although less likely, pulmonary embolism can present with sudden onset of cough, mild fever, and severe back or chest pain. It's a life-threatening condition that requires immediate medical attention.
Tuberculosis (TB): TB can cause a chronic cough, which may initially be dry, and can be accompanied by fever, night sweats, and back pain due to spinal involvement (Pott's disease).
SARS-CoV-2 (COVID-19): Given the global pandemic, COVID-19 should be considered, especially if the patient has been exposed or has risk factors. It can present with a wide range of symptoms, including dry cough, fever, and body aches.

Lymphoma: Certain types of lymphoma can cause systemic symptoms like fever, night sweats, and weight loss, along with cough and back pain if there is mediastinal or spinal involvement.
Sarcoidosis: This condition can cause cough, fever, and musculoskeletal pain, among other symptoms, due to granulomatous inflammation in various parts of the body, including the lungs and bones.