Conjunctivitis and eye swelling/drainage can be signs of a chronic respiratory disease. Terramycin (oxytetracycline) is one of several drugs that will treat symptoms, but if it is a disease such as MG, it will not be cured. The chicken would be a carrier. Testing is the only way to make sure. I would keep the chicken isolated away from the flock while I treated with the antibiotic. There is also Terramycin eye ointment that you can use in the eye along with antibiotic in the water. Here is a link with a list of many common respiratory diseases including symptoms and treatment:
http://edis.ifas.ufl.edu/ps044