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Your child seems to be suffering from Acute Infective Diarrhea/ Acute Gastro-Enteritis.
Most of the times the diarrhea are viral in origin and it improves with in 3-5 days without any antibiotic therapy.
The only thing that needs to be kept under consideration is that the child doesn't get dehydrated.
Antibiotics are required in cases where there is associated cramping, blood in stools or fever.
Since your child has 4th day of diarrhea and that too with fever, i would recommend for him antibiotics like Ofloxacin and Ornidazole for him.
You should also take Probiotics containing Lactobacillus which helps a lot. You can give him yoghurt that also acts as a very good natural probiotic.
In case he has persistent vomiting's he would require anti-emetics like Domperidone and Ondansetron.
He is lethargic probably because he is dehydrated. Make sure about his hydration status. You can give him Oral Rehydration syrup (ORS) for the purpose of re-hydration.
Make sure he is passing urine frequently. If the urine is yellowish in color, it indicated persistent dehydration or jaundice.
I hope it helps.
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