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Vomiting can occur from a few causes.
Common causes are an infection, indigestion.
As he had fever initially, there can be a viral illness.
Though viral illness recover within a few days, sometimes it can be prolonged.
Gastritis, reflux, hepatitis
etc. can be associated with it.
Along with bland diet, Antacid or Ranitidine can be tried for a few days. They can help in gastritis.
Non abdomen issues like urine infection, ear issues, abdominal migraine etc. can also cause vomiting.
I think his pediatrician did not find any sign for those.
Other tests like urine analysis, blood metabolic panel can be considered, if those were not taken earlier or if his doctor thinks necessary.
If no apparent cause is there then it can be cyclical vomiting where the cause is not clear.
Some triggers like cold, allergy
, weather change, food like cheese, chocolate or overeating, physical stress etc. can precipitate the symptoms.
But he is on bland diet diet for a few days.
Please try to look for any such triggers.
If the symptom continues, you can take a consultation with a pediatric gastroenterologist too.
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Wish his healthy life.