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Hollow metal nanostructures are fascinating because of their unique and surrounding environment-sensitive localized surface plasmon resonances (LSPRs). Herein, we have investigated the hollow silver nanoshell (HSN) sensitivity of different inner core radii and shell thicknesses with respect to change in surrounding medium refractive index. Also, we have shown that the extinction peak of HSNs can be fine-tuned in the visible region as well as biological windows by manipulating the size parameters. Moreover, an enhancement in refractive index sensitivity of 133 to 283 nm/RIU can be achieved in the biological windows by thick hollow silver nanoshells in comparison to thin ones. To achieve a comprehensive study, the sensitivity of homogeneous LSPR extinction inflection points with change in refractive index is also investigated. A consistent improvement in bulk refractive index sensitivity of 36% and 15% is predicted with thick and thin shell layers, respectively. Finally, thick HSNs showed higher refractive index sensitivity when compared with thin ones. Moreover, we envision the idea of more than one molecule detection by tracking the curvature changes. Therefore, we provide a deeper insight into the refractive index sensitivity of homogeneous LSPR inflection points for their use in LSPR-based sensors. [ABSTRACT FROM AUTHOR]