The family says the baby was given an iv drip and administered the antibiotic azithromycin and almost immediately had a negative reaction.
"Right away I see his eyes turn blue and his lips were blue," said the boy's mother Ummay Sultana.
Soon after the baby lapsed into a coma, and was placed on life support until Tuesday.
The family now says Amaan died of an overdose of the antibiotic.
And a hospital discharge summary appears to support that claim, acknowledging 500 mg of the azithrromycin was given in error.
His parents say it should have been 80.
"They have no professionalism?my baby's only 6 months old," said the father.
In a statement, Brookdale Hospital would only say "We are investigating the circumstances of this tragic incident and express our condolences to the Ahmmad family."
But the grieving parents are demanding answers now.