From what you have said there is NOWAY in burning hell I would of left that ED with out it being the case of being moved to the Childrens ward. MOTHERS AND FATHERS KNOW THEIR BABES BETTER THEN A DOCTOR. I would suggest taking her back and demanding that they do something and refusing to leave till they do.

(I had to take my 5yo niece when she was a few months old- drs said just viral but we suspected minigicolcle?sp cause of spiking temp and purple rash- they soon listened when I threatened legal action for medical negligance).