Brief Answer:
Most likely cyclical vomiting syndrome,Repeat WBC count

Detailed Answer:
Hello

Thanks for asking on this platform

I have gone through the details and to me it appears to be cyclical vomiting syndrome.
Frequent, repetitive episodes of vomiting with normal health between the episodes is common in children with cyclical vomiting syndrome.

The diagnosis of cyclical vomiting syndrome can be made only after thorough clinical and laboratory investigation. All these investigations (liver function test,kidney function test, USG abdomen,electrolytes,blood gas etc) should be within normal limit.

Here the main aim of management is behavioral and pharmacological therapy with avoidance of trigger, if any. This is more common if there is family history of migraine.

I suggest you to consult your pediatrician regarding evaluation and management.
Raised white blood cell count with increased proportion of neutrophil can be there due to infection. In absence of fever or any other symptoms chance of infection is less.Still I would like to get C-Reactive Protein level done if not done earlier to rule out any bacterial infection.

If C Reactive Protein is normal, get repeat WBC count done after one week and if problem persists then it can be due to leucocyte adhesion deficiency (LAD) a immunodeficient condition.

I would like to know if there is history of delayed fall of cord as in case of LAD in most of the babies there is history of delayed fall of umbilical cord.

I hope this helps.
Please let me know if you have any more query.
Regards

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