Factitious Disorder Imposed on Another (Munchausen Syndrome by Proxy): This condition, where a caregiver fabricates or induces illness in a child for attention and sympathy, is a strong consideration given the discrepancy between the parents' claims of fever and vomiting and the lack of clinical evidence in the pediatric department.

Viral Gastroenteritis: Although the baby appears well, viral gastroenteritis could explain the vomiting, and the fever might have resolved by the time of examination.
Acute Viral Infection: Many viral infections can cause transient fever and vomiting, which might have resolved quickly, leaving the baby appearing well by the time of medical evaluation.
Gastroesophageal Reflux Disease (GERD): This condition could lead to vomiting, which might be mistaken for a sign of infection or other acute illness.

Bacterial Meningitis: Although the baby appears well, bacterial meningitis can present subtly in infants, with nonspecific signs such as vomiting and fever, which might have been present earlier.
Urinary Tract Infection (UTI): UTIs can cause nonspecific symptoms in infants, including fever and vomiting, and are important to diagnose to prevent long-term complications.
Intussusception: This condition, where a part of the intestine slides into an adjacent part, can cause intermittent vomiting and might not always present with the classic triad of abdominal pain, vomiting, and bloody stools.

Inborn Errors of Metabolism: Certain metabolic disorders can present with episodes of vomiting and might be considered if other diagnoses are ruled out and the baby has recurrent episodes.
Congenital Anomalies of the Gastrointestinal Tract: Conditions like pyloric stenosis or other congenital anomalies could lead to vomiting but would typically have other associated findings on physical examination or imaging.