Actually, I wouldn't give her an antibiotic to prevent respiratory infections.
Note - the way I'm reading this, you're saying that her nostril cut is infected and inflammed (possibly preventing good breathing), not that she has a snotty nose. Yes?
Giving antibiotics without there being that type of infection there is - well it's one of the reasons we're having problems with super-bacteria these days. Also, birds are more sensitive to all chemicals especially antibiotics which kill a lot of the very necessary good bacteria needed for their unique avian metabolism. Antibiotics don't say "that's a good one, and that's a bad one". So you might end up with a bird who wasn't going to have a respiratory illness but ends up with a digestive tract infection instead because of good-bacteria die off.
If you feel she has an infection that isn't responding to the antibiotic ointment, then it's possible to give an injectable wound-specific antibiotic such as Procaine Penicillin every other day at a dosage for her weight. That's protocol for wounded waterfowl if their wounds are infected or there's a possibility for an infection that you can't see behind the eye or wounds.
Then boost her immunity to prevent secondary stress-induced respiratory and other problems. Boost her nutrition by giving her a non-medicated baby food, or game feed, if you happen to have some. If this sort of thing happens, I might pick up the little paperbags they make for people at the feedstore who don't have many chicks. You can also give her a boiled egg yolk a day to boost her nutritional intake. Because she's in distress, I'd give her a probiotic every other day or every third day. Plain yogurt is great for this for an adult bird not experiencing any digestive issues yet. Mix that, the yolk, some crumbles, some of your good vitamin water youre making - bingo. I find that few birds can resist regressing to baby food.
Let us know if you feel you need to treat the wounds' possible infections with injectables. We can help with that.
Also realize that if her vision is not there (and it takes a while for eyes to get better, if they do at all, vision wise) then she'll be depressed. If she's eating and drinking at all with your help, I'd consider that progress. If she truly wanted to die I think she might have before. You're the one with the good instincts here. What do you feel she wants? She also might have a decreased appetite because of possible visual impairment. Something to consider.
Personally, I think standing and moving around a bit sounds alright considering. Not as hopeful as we all wish. But it does take a while for them to feel better. I wonder if you could do anything to sort of perk her up? Is she missing her buddies possibly?