You are doing the right thing by making sure you are properly treated and have the
gist of your situation. You must be sure to follow up because studies have shown, unfortunately, that gonorrhoea is becoming resistant to antibiotics. This is why it's often referred to as "the clap" because people think that they have been treated for it when they weren't and assumed that it some how returned.
As far as any other STIs goes, there is an incubation period as cutegirl provided.