I mean you are trying to save her life, I cant help myself from stressing out too when they are sick. I treat five sick chickens a day, and they all over the house and even laying eggs in my bed because I have too many lol.
I think you are set with the ivermectin and corid instructions you said.
The antibiotic, it would be best to give the medicine as (i think) eggcessive said. But I tried to explain that is how it should be, but you said you already put 500 mg into a gallon. I keep some antibiotics refrigerated to preserve them, but I dont think it will spoil in the water it is designed for fish water right?
A full dose of the powder in smaller amount of water is how the medicine is designed to work, its called immediate release and the powder you have is designed for immediate release a single dose. If you give the dose eggcessive said, it would be 2x per day 10 mg. There isnt a correct length of time published.
The way you set it up in the water (500mg in a gallon given all day) is called sustained release. Corid has to be given through sustained release and the fresh water has to be removed so the corid is delivered properly. But it really wouldnt hurt to give your antibiotic that way, but it is not per the instructions, more difficult, and prone to error in the dosage.