We present a generalizable approach for designing biosensors that can continuously detect small-molecule biomarkers in real time and without sample preparation. This is achieved by converting existing antibodies into target-responsive "antibody-switches" that enable continuous optical biosensing. To engineer these switches, antibodies are linked to a molecular competitor through a DNA scaffold, such that competitive target binding induces scaffold switching and fluorescent signaling of changing target concentrations. As a demonstration, we designed antibody-switches that achieve rapid, sample preparation-free sensing of digoxigenin and cortisol in undiluted plasma. We showed that, by substituting the molecular competitor, we can further modulate the sensitivity of our cortisol switch to achieve detection at concentrations spanning 3.3 nanomolar to 3.3 millimolar. Last, we integrated this switch with a fiber optic sensor to achieve continuous sensing of cortisol in a buffer and blood with <5-min time resolution. We believe that this modular sensor design can enable continuous biosensor development for many biomarkers.