I am so sorry about this little baby!
I am really not sure what is causing this. I have never dealt with a chick so small with an eye infection. Adults yes, chicks no. So all I can really do is give you some ideas as to what it MIGHT be.
This doesn't appear to be effecting the eye ball itself but rather the surrounding tissues.
Mites, which are common in broodies nest boxes will cause eye infections like this. The mites burrow in around the eyes and cause infections. I would check the broody too for mites. Check around her vent, behind the neck and under the wings. Look for eggs at the base of the feathers near the skin...looks like dirt. If you feel they do have mites, and I have never dosed a tiny chick like this, but you might try some Ivermectin Liquid Pour On for Cattle. I am guessing at only 1 drop behind the neck. Make sure it gets on the skin as on the feathers and it does no good. It needs to get absorbed by the skin.Dose the broody too....6 drops behind the back of the neck on the skin for a standard sized breed, 3 for bantams. Then clean out the nest box bedding well.
Another possibility is the chick has some sort of sinus infection behind the eyes. If the eggs were really dirty during incubation, something might have caused her to contract an infection. You might then try some antibiotics. Tylan soluble, in the water, is great for sinus infections.
Are there other chicks in with her? She may have gotten pecked around the eye or possibly poked by some straw? If this is the case, it should heal on it's own.
You might keep some vitamins or probiotics in the water. Either of these are great to pump up the immune system so they can fight these things off internally. Chicks haven't quite yet developed much of an immune system, but will help build it up faster right now.
Other than these suggestions, I really do not know, I have never had this happen to me.
Good luck with her. She is so tiny and sweet, I hope you can get her back to good health soon!
