Hi there!
Thanks for asking here. Now you can get a range of opinions.
First, daily use a sterile eye wash (boric acid is an active ingredient - buy at the pharmacy, don't make your own as it won't be sterile). Use that to clean the exudate away from the eye daily. Let that sit 10 minutes before applying the eye drop.
Do your eye drop daily.
On the VetRx, you can use that diluted* to swab the nares (nostrils), the cleft opening in the roof of their mouth (called the 'choana'), and underneath their eyes. For each new spot, use a new q-tip end. If you were treating two birds, you'd want a completely new q-tip between birds.
*VetRx dilution and use: On VetRx, I use a few drops of VERY hot water, a few drops of VetRx, in a cup. Use something non-absorbant to stir well. This will cool the VetRx mixture to warm and emulsify the vetrx oil into the water.
Separate this baby out. Make sure she eats and drinks. To facilitate ocular healing and take care of any undiagnosed vitamin A deficiencies, I'd give her polyvisol vitamins daily for a week. Vitamin A deficiencies have these same symptoms and aren't entirely uncommon particularly in young birds. (More oh "why" later in this thread.) You don't want to overdo vitamin A as it's an oil vitamin.
All of your babies would likely benefit from some supplementation which can be done with a poultry vitamin/mineral powder in the water. Or alternately, you can use cod liver oil or fortified (read the label) wheat germ oil on the feed. You'd only use a few drops mixed into a small batch of crumbles. Mix those crumbles with a little water and make a damp (not wet) mash. Withdraw their feed 20 minutes before feeding the mash and make sure all get some. Alternately, you can put wheat germ oil into a travel sized misting bottle and spray on the top of their crumbles first thing in the mornning. Use the cod liver only twice weekly - or - the wheat germ oil three times weekly - or - the vitamin/mineral powder in the water. Don't use any of those three together.
Make sure that your feed is less than a month old, stored in an airtight and light-proof container in a cool area. Only feed the amount of crumbles that your babies will eat daily, re moving the remaining powder when you replace them. These actions will help keep the Vitamin A in your feeds more active and available.
If you feel that the baby might have a respiratory infection (it's possible, though not proven yet) you can use Tylan50 injectable diluted with water as an eye and sinus flush. PM me if you need instructions on that.
I don't believe I'd yet treat her with systemic antibiotics. I'd try the vitamin supplementation, separation, the VetRx, and the feed control and see if she improves.
Incidentally, any time a bird has sinus issues, always give them some yogurt as a supplement. (Again all your babies will benefit from this.) 1 teaspoon per 6 small babies. AT her age, a half teaspoon per bird would be fine - or even a teaspoon. Some like it straight, others you have to hide in that damp mash. Mix the yogurt with some water, mix that with a small amount of crumbles, let soak 10 minutes. Or mix with some mashed yolk of a boiled egg or a whole egg boiled and made into 'meal' in the food processor. (Refrigerate what you don't use that day for use throughout the week.) The eye drains through the roof of the mouth into the digest tract, throwing off the good bacteria there. Using yogurt will replace the good bacteria. (Just don't use yogurt if you end up treating with a -mycin or -cycline drug.)
Also be sure to do the sick chick's chores AFTER you do the other babies. that way if she has anything, you won't keep challenging the healthy babies with it.
SUMMARY:
Sick chick (isolated):
polyvisol drops - 2 drops per beak daily for a week; taper off thereafter
yogurt - use daily for a week; taper off daily thereafter.
Saline eye wash (boric acid): use to clean eye daily 10 minutes before using ointment.
Ointment: Continue to use once or twice daily.
boiled/mashed egg: as needed to hide healthy stuff.
VetRx: nostil swab, choana swab, under eyes daily once.
All chicks:
Vitamin/mineral package in water for a week.
Yogurt a couple of times this week.
boiled/mashed egg: as needed to hide healthy stuff.