I was at a performance of Otello with Placido Domingo playing the title role. During a scene with Iago, Domingo suddenly stopped singing and walked off stage, looking somewhat upset. The poor baritone was left standing there, not knowing what to do, until the curtain came down. About ten minutes later an announcement was made that Domingo had a sore throat (coulda' fooled me -- he sounded just fine), but that he was willing to continue with the performance. The house lights came up and we got an unscheduled intermission, and then the opera (slightly abbreviated) resumed with Domingo returning to the wild applause of the audience.
And that is how a singer should handle a sore throat.