She might have a scratch on her eye. Usually it will show up sooner that 5 weeks, but another chick cold have pecked her. You can try putting opthalmic antibiotics in the eye for 5 days. I used the cheap triple antibiotic stuff from the dollar store.
A picture may help. Are you seeing any others that look the same? Respiratory diseases such as MG can start out with eye drainage, swelling around the eyelid or face, and nasal drainage. But injuries are also a possibility. If there is thick or pus drainage, I would clean out the eye with saline, and apply antibiotic ointment as ochochicas has advised. If it smells bad or there is a cough or swelling around the eye, I would consider giving an antibiotic such as Tylan or oxytetracycline. Here is a link about the common respiratory diseases: http://edis.ifas.ufl.edu/ps044