Ouch. Sorry to hear that.
It's obviously doctor time, including telling them about your worries about your eye. Different areas have different strains of gonorrhoea, so you want someone who is up to date with the local situation.
As far as telling partners, I do like the idea of doing it anonymously. If you go to a sexual health clinic, they may have a contact tracing service that will do it for you. Otherwise, even Mr Pop-out-while-she-sleeps will be better off testing and knowing sooner rather than later. It may avoid her being infected, for example.
(For those who have not been keeping track of his various usernames over the years, Blaine is male and in the US.)