Does anyone know what the bacteria/micro-organism might be?
As I mentioned, Efflux Pump Inhibitors can make antimicrobials considerably more effective by preventing them from eliminating toxins to them, antimicrobials.
Reserpine (Rauwolfia serpentina and Rauwolfia vomitoria) is one of the most widely effective EPI's working against multiple Efflux Super families. It does have some side effects which made me not want to use it. It does appear to be slightly alkaline, an alkaloid. It does affect various binding sites for epinephrine, dopamine etc and has mood altering, sedating, bradycardia effects which is why I did not want to use it. It can lower blood pressure which the drug form was used for before other drugs became preferred due to reserpine side effects.
You might be able to boil some root to extract reserpine and reduce it. I did come up with the following article which I have not yet read, which might of shed more light on extracting the alkaloid. Ethanol etc might not be what is wanted seeing as it would be used in the eye unless it could be eliminated. There are ideas on how to do this online. http://sci-hub.hk/10.1080/01496395.2011.635623
[EDIT] alkaloids are not well extracted using water unless the water is acidic. Acetic acid is sometimes used. Maybe lemon or white vinegar which contains acetic acid. The pH could later be increased to neutral/7 pH using a base/alkaline such as sodium bicarb.
Trying some rubbed onto the eye lid and also some of the Antibiotics you have, might have greater effect. EPI's can make ineffective Antibiotics effective once again. If that had no negative effects, then adding a small/diluted amount into the eye and again followed by the Antibiotics . If you try this, then start with the smallest amount you can and very slowly work up. I do think that EPI's are the thing to use in this case, and reserpine is as I mentioned the single EPI with the widest range of effect. It can have effect against a wide range of micro-organisms.