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Cold peripheries along with fever
is usually suggestive of bacterial sepsis
and considering that your child is complaining of chills
, it's best to take him to an urgent care facility for a thorough evaluation and appropriate antibiotic prescription .
It's good that you are keeping him well hydrated with plenty of fluids .
However he might need to be investigated further for confirmation of diagnosis and require an antibiotic .
So kindly seek a pediatrician
consultation as soon as feasible .
Wishing your child a speedy recovery .