Need advice please

So my daughter is 13 months old and a healthy peanut. Well, she started getting fevers of 101.5, then they started reaching 103. So one night i called the ER and they had the pediatrician call me. I gave her my daughter's symptoms and she "diagnosed" her with the flu. She told me to give it a week then bring her in. Well we were alternating Tylenol and ibuprofen. Pushing fluids. Until night 4 her fever spiked to 106.5 and she had trouble breathing. My s/o and i rushed her to the hospital and they had to do a chest xray. She has pneumonia.

I feel like the world's shittiest mom for not taking her in sooner.. They gave her amoxicillin and that helped for a few days until she spiked again. The doctors ran a blood and her white blood cells are extremely low and she's at risk for an infection. So they decided to stop the amoxicillin and gave her a stronger antibiotic and we go back today which is the day after the first blood test for another one and I'm just praying that they see some sort of result.

When I gave her her first dose yesterday she improved by that I mean she was up playing, smiling, eating. I just need some words of encouragement this poor munchkin has been sick for almost a week and a half two weeks. She had just got over the croup a week prior to the fevers.

Im a first time mom, and feel so helpless because shes so exhausted but so restless at the same time..