I mean this in the nicest way:
NO! Stop cycling through the antibiotics and go get the tylan! And get some low dose aspirin (81mg) while you're out. It's important to not tiptoe through things experimentally when you see symptoms that call for specific treatment and your beloved bird is weak and barely hanging on.
Sulmet is HARSH on their systems and she's already had multiple meds and is WEAK.
Whatever you do, you must get some ACTIVE CULTURE yogurt and give it to her to improve her gut health, as the antibiotics she's had will have killed off all of the beneficial bacteria in her intestines and weakened her. Your path right now is toward her having an overgrowth of the e. coli that is naturally present, and that could kill her.
I'd get the Tylan, but also give her dry oatmeal in yogurt mixed with her feed.
I know we lean on alllll sorts of ideas when our beloved birds are down, but you mustn't weaken her by going through meds that aren't the right type for the symptoms or indications.
Sulmet is a sulfa based drug and isn't a broad spectrum, timed release like Tylan. You can put the Tylan in her water to dose her, as it can cause tissue damage if injected undiluted, and dilution is a pain when you haven't a clinical set-up.
I hope she gets better soon! Best of luck!