D.B.
I understand your concern over not spraying her room with pesticides... but you're talking fire ants which are bad. I'd spray just so they don't return any time soon and bite her again. They are almost as bad as spiders. (We get black widows here and have caught one in the house - so i spray my kids' room for that. black widow bite = er visit for us)
But I'd definitely move your daughter into another room to sleep for at least the next few nights while you find something to get rid of the ants until your sure there's no more of those ants in her room.