It's good that she is eating/drinking and that you are treating her. Personally, yes, I would flush the eye and remove any pus that is seen, then apply an eye ointment at least once a day if not more.
Hi
@KLamb Sorry to hear that you have some sick chickens. Respiratory illnesses are very contagious and easily spread. Corid is Amprolium which is a Coccidiostat - this only treats Coccidiosis and is not an antibiotic.
For Terramycin eye ointment or Veterycin look at feed stores like Tractor Supply. You can also order online through places like JeffersPetSupply or FirstStateVet.
If you feel that she needs antibiotics in addition to the topical treatment, you can use injectable Tylan50 which is also found at most feed stores.