This research examines plasmon-exciton coupling in nanostructures consisting of a plasmonic metal core and a dye-based shell. We employed the finite-difference time-domain (FDTD) approach to examine the optical characteristics of several nanowire shapes, encompassing circular and elliptical cross-sections. The optical properties of plasmonic metals (gold and silver) and dye molecules are described using the Drude and Lorentz models, respectively. The results propose that various elements, including the characteristics of the nanoparticles (type and size) and the refractive index of the surrounding environment, have a considerable impact on both the surface plasmons and the type of coupling (strong or weak). By examining the oscillator strength and damping coefficient within the framework of the Lorentz model applied to the dye shell, it is evident that enhancing the oscillator strength and reducing the damping coefficient can sharpen the dip formed due to strong coupling. Furthermore, the insertion of the shell component plays a vital role and introduces additional degrees of freedom for tuning the plasmonic response, enabling the excitation of hybrid plasmon-exciton modes and potentially broadening the spectral range of detectable signals. in broadening the range of surface plasmons. The present study investigates the quality factor, figure of merit and sensitivity of two distinct structures, specifically nanowires with circular and elliptical cross-sections, for various types of cancer. The research demonstrates how tunable optical properties of multilayer nanoshells, influenced by the outer and core radii, enable precise control of LSPR peak positions, with blue and red shifts governed by dielectric environment changes and core radius variations, respectively, offering potential for advanced plasmonic applications Moreover, we noted a significant correlation between the LSPR peak position, the core radius, and the surrounding refractive index, facilitating accura