Changes in personal protective behaviors driven by media influence contribute to epidemic prevention and control, whereas limited medical resources constrain the effectiveness of such interventions. In this study, we propose a novel influenza transmission model with the media impact and limited medical resources. Theoretical and numerical analyses reveal some complex nonlinear dynamics, including saddle node bifurcations, forward and backward bifurcations, and both subcritical and supercritical Hopf bifurcations. Besides, two types of bistable scenarios are identified: bistability of a disease-free equilibrium and an endemic equilibrium, and bistability of two different endemic equilibria. In addition, we fit the model to the monthly new influenza reported case data from August 2023 to October 2024 in Jiangsu, China, where the fitting results successfully capture the observed epidemic trends. The estimated basic reproduction number $\mathcal{R}_0 = 1.2183 > 1$ implies sustained transmission. Finally, sensitivity analysis suggests that effectively controlling influenza transmission can be achieved by decreasing the population input rate, transmission rate, awareness loss rate, and medical saturation constant, as well as increasing the awareness transmission rate, media response intensity, and maximum recovery rate. These findings highlight the critical role of combining public awareness initiatives with enhanced medical resource allocation to strengthen influenza prevention and control efforts.