Terramycin (oxytetracycline) or vetracyn are what is most commonly used to treat eye infections. You can usually purchase it at feed stores that cater to larger livestock or poultry, some drug stores carry it also.
Personally I highly doubt this is an eye infection, although it isn't a bad idea to have terramycin on hand because eventually you'll probably have to deal with one. Also I've not found any research or advice that suggests it is safe to use such a strong antibiotic on a chick so it's probably best just to let this one ride unless the chick begins to show anymore symptoms.
Eye infections will almost always be accompanied by swelling around or of the lids and drainage that quickly builds a crust. That crust can easily cover the whole eye and often will damage their vision in the affected eye if not treated quickly enough can even kill them. So Terramycin or vetracyn are good to keep around or at least know where you can find them on the shelf should you need them. Don't be surprised that it runs about $30 for a small tube.