I read your story and it broke my heart.
One thing I learned in this life - never put your life or life of your family in a hands of one Dr even if you trust him/her a lot.
Obviously here something more serious than just infection (they gave her antibiotics). Search... If you need to take her to the best of the best, just do it.
I and my family went through a lot and still go and everything could be so much easier if I would go right the way not to a local Dr but to the places I go now. Does not matter how much it costs, how much time it takes (I am far from being reach) but what a difference!
Good luck to your little one and to your family. Don't give up and if you see something is not right, don't take no for an answer.