so happy it's resolved and you're both home and healing.
IF her infection was less advanced, had had less time to settle in, and IF she wasn't still recovering from the additional stress of the hospital ordeal, and IF your house wasn't in stress mode from the whole ordeal (and I mean all three IFs at once!), then I could understand possibly not giving her these antibio, and trying to find ways to help her brand-new, not really very strong immune system try to fight it off naturally.
BUT that's not the case. There are so many other factors weakening her ability to deal with this right now. It sounds like she honestly can't get rid of this infection on her own. IMHO, as scary as antibio are, this is one of those cases where I'd be very, very grateful for them. If the infection has reached her kidneys, this is not something to play with. That's officially the bigger threat, IMO.
As a way to make sure you've done everything you can, I'd call back the prescribing doc and just verify that there's nothing else you can give, in light of the bilirubin issue BUT I'd keep her on them while I was looking into that. Again, infection in the kidneys just isn't something that leaves you much wiggle room at this age.
I hate to say it, but sometimes we have to choose the lesser of two evils. And speaking from experience in my own childhood, it can be much, much better to live with some aftereffects than the alternative.
I really, really wish you peace right now. You're working so hard to keep this little one safe, and I can hear that you're starting to feel like no option is safe. I've been there, and it's a really scary place. Know that whatever happens, you're a great mama, you've done all you can, and trust that this is going to work out for the best.
i'm pretty anti meds, and scared of side effects, but thank goodness for antibiotics! these are the rare situations where i really see the application and would use them. and i treat everything w/ cod liver oil.
i'd actually reach out and ask those around you to pray for your little one and help support her in that way so whatever you do next she's got people's hearts reaching out to her. you can only do so much. double check w/ your doc, get the practical physical stuff addressed, and then surround her with all the love and prayers you can. it's not scientific, many people scoff at it, but sometimes there's a limit to how much we can really completely take control of in the physical.
so sending out prayer for you both from here! and that your doc will stay on top of things as well.