Infective conjunctivitis in 19 week old - any suggestions?

[IsItMeOr]

My DS has had watery eyes since Sunday before last. Took to GP on the first Monday and she says infective conjunctivitis, clean it with boiled water. If it gets green gunge, use these antibiotic drops. Ah, says IsItMeOr, green gunge that I cleaned out this am, so starts using drops. By Thursday, eyes stop watering, so stops using drops on Saturday. By Sunday, eyes look a little "full" again, and properly leaking on Monday again.

Am now wiping out with boiled water, washing everything he touches after one use where practical.

Poor little mite is on/off whingey, and not his usual cheery self.

Is there anything else I should be doing? Guess I go back to GP on Monday if he's still runny?

Thanks!

Soory, also meant to ask whether all that washing is for his benefit (does he reinfect himself?! I am rubbish at human biology, can you tell?) or to stop us from getting it? If latter, I probably don't need to be quite so keen!