Yes, a thin small "fingernail" strip is all that is needed. It will melt in the eye, no problem.:)
Also check her eye closely for a piece of feather or fluff in her eye which can cause irritation. I've had that happen and use small scissors to cut it down as necessary.
It might be environmental since there are no other symptoms and your other birds arnt showing symptoms of a respiratory disease.
Ammonia fumes from soiled bedding can be a cause, pollen, dust or debris in eyes from dust bathing, feed dust, scratched eye etc...
Flush the eyes with saline...