Sexually transmitted infections (STIs) continue to present a complex and costly challenge to public health programs. The preferences and social dynamics of a population can have a large impact on the course of an outbreak as well as the effectiveness of interventions intended to influence individual behavior. In addition, individuals may alter their sexual behavior in response to the presence of STIs, creating a feedback loop between transmission and behavior. We investigate the consequences of modeling the interaction between STI transmission and prophylactic use with a model that links a Susceptible-Infectious-Susceptible (SIS) system to evolutionary game dynamics that determine the effective contact rate. The combined model framework allows us to address protective behavior by both infected and susceptible individuals. Feedback between behavioral adaptation and prevalence creates a wide range of dynamic behaviors in the combined model, including damped and sustained oscillations as well as bistability, depending on the behavioral parameters and disease growth rate. We found that disease extinction is possible for multiple regions where R0>1, due to behavior adaptation driving the epidemic downward, although conversely endemic prevalence for arbitrarily low R0 is also possible if contact rates are sufficiently high. We also tested how model misspecification might affect disease forecasting and estimation of the model parameters and R0. We found that alternative models that neglect the behavioral feedback or only consider behavior adaptation by susceptible individuals can potentially yield misleading parameter estimates or omit significant features of the disease trajectory.