Viral Gastroenteritis: This is the most likely diagnosis given the symptoms of fever, vomiting, and the presence of sinus tachycardia, which can be a response to dehydration and fever. The elevated WBC count with a lymphocytic predominance also supports a viral etiology.

Bacterial Gastroenteritis: Although the lymphocytic predominance might lean more towards a viral cause, bacterial gastroenteritis cannot be ruled out without further testing, such as stool cultures. Symptoms like fever, vomiting, and an elevated WBC count can also be present in bacterial infections.
Food Poisoning: This could be another likely diagnosis, especially if the patient has a history of consuming potentially contaminated food. The symptoms and lab findings could align with food poisoning, which is often caused by bacterial toxins.
Urinary Tract Infection (UTI): Although less likely given the gastrointestinal symptoms, a UTI could present with fever, tachycardia, and an elevated WBC count. It's essential to consider this, especially in patients with risk factors for UTIs.

Appendicitis: Although the primary symptoms do not directly point towards appendicitis, it's a condition that could potentially present with fever, vomiting, and tachycardia, especially if the appendix is in an atypical location. Missing this diagnosis could lead to severe consequences, including perforation and peritonitis.
Septicemia: The presence of fever, tachycardia, and an elevated WBC count could indicate sepsis, especially if the patient shows signs of organ dysfunction. Early recognition and treatment of sepsis are crucial to prevent high mortality.
Meningitis: Although less likely given the absence of specific neurological symptoms, meningitis is a critical diagnosis not to miss. It can present with fever, vomiting, and tachycardia, and the consequences of missing this diagnosis can be fatal.

Toxic Shock Syndrome: This is a rare but life-threatening condition that could present with fever, vomiting, tachycardia, and an elevated WBC count. It's often associated with bacterial infections, such as those caused by Staphylococcus aureus or Streptococcus pyogenes.
Hemolytic Uremic Syndrome (HUS): Typically seen in children, HUS can follow certain bacterial infections (like E. coli O157:H7) and presents with a triad of hemolytic anemia, acute kidney injury, and thrombocytopenia. While rare and less likely given the initial presentation, it's a diagnosis to consider in the appropriate clinical context.