Plasmonics and core-shell nanomaterials hold great potential to develop pharmaceuticals and medical equipment due to their eco-friendly and cost effective fabrication procedures. Despite these advancements, combating drug-resistant bacterial infections remains a global challenge. Therefore, this study aims to introduce a tailored theoretical framework for a one-dimensional (1D) photonic crystal biosensor (PCB) composed of (ZrO2/GaN)N/defect layer/(ZrO2/GaN)N, designed to detect Gram-positive and Gram-negative bloodstream bacteria employing the transfer matrix method (TMM). In addition, using the finite difference methods (FDM), the photothermal inactivation of bloodstream bacteria with plasmonic core-shell structures (FeO@AuBiS2) was explored using key factors such as light absorption, heat generation, and thermal diffusion. By incorporating six dielectric layers and contaminated blood into the proposed PCB, a maximum sensitivity of 562 nm per RIU was recorded, and using rod-shaped plasmonic core-shell structures, 5.8 nm-1 light absorption capacity and 152 K change in temperature were achieved. The maximum detection sensitivity, light absorption, heat conduction and heat convection capacity of the proposed 1D PCB and plasmonic core-shell show an effective approach to combating drug-resistant bacteria.