What is done if strep throat doesn't go away with a full course of antibotics ?

Several possibities: You were re-exposed and reinfected ( using the same toothbrush or kissing your asymptomatic partner can do this). You can also have another issue at the same time.Mono and strep can occur concurrently. Some people reinfect so easily that a 2 step treatment protocol using a penicillin drug followed by Rifampin is occasionally used.