What makes you believe that you have an eye infection?
The eyes are sensitive and many antimicrobials are risky. Essential oils can be very strong but not suitable for the eyes.
Potassium Iodide might have some effect, it is clear so will not stain like lugols.
DMSO has antimicrobial effects. It is used in research for solubilizing various compounds when testing their antimicrobial properties but because it has been found to possess antimicrobial effects itself, researchers now try and limit it's use.
DMSO would help drive any other antimicrobial into the eye tissue which might help enhance it's effect. You would need to check whether it is safe to use in the eye.
BTW Microorganisms can become immune to silver despite what people on this forum try to claim. I have tried Efflux Pump Inhibitors with Silver and it had an effect which it did not have when used on it's own. That just shows that they can and do become immune to silver.