Viral Respiratory Infection: This is the most common cause of fevers, cough, and vomiting in infants, with viruses such as respiratory syncytial virus (RSV), influenza, and adenovirus being frequent culprits. The symptoms presented are typical for a viral upper respiratory infection, which is prevalent in this age group.

Acute Bronchiolitis: Often caused by RSV, this condition presents with cough, wheezing, and sometimes vomiting, especially in infants under 2 years old.
Gastroenteritis: Viral infections can cause gastrointestinal symptoms like vomiting, alongside fever and sometimes cough, if the infant has a concurrent respiratory infection.
Pneumonia: Bacterial or viral pneumonia can present with fever, cough, and vomiting, especially if the infant is not feeding well or is showing signs of respiratory distress.

Bacterial Meningitis: Although less common, bacterial meningitis is a life-threatening condition that can present with fever, vomiting, and sometimes cough, if there is associated pneumonia. It requires immediate medical attention.
Urinary Tract Infection (UTI): UTIs can cause nonspecific symptoms in infants, including fever, vomiting, and sometimes cough, if the infection has spread to the kidneys.
Sepsis: A systemic infection that can present with fever, vomiting, and cough, among other symptoms. It is critical to identify and treat sepsis promptly to prevent serious complications.

Congenital Heart Disease with Infection: Infants with undiagnosed congenital heart disease may present with symptoms of infection, including fever, cough, and vomiting, due to increased susceptibility to infections.
Inborn Errors of Metabolism: Certain metabolic disorders can present with nonspecific symptoms like vomiting and fever, especially during times of stress or infection.
Tuberculosis (TB): Although rare in infants, TB can cause a range of symptoms including fever, cough, and vomiting, particularly if the infant has been exposed to someone with active TB.