To detect anemia and diabetes type from in vitro samples, a simple structured solid-core photonic crystal fiber (PCF) refractive index biosensor based on surface plasmon resonance (SPR) was designed and investigated. Silver and $TiO2$ nanolayers were coated over the PCF for external sensing. The sensing characteristics of this sensor are analyzed using the finite element method (FEM). The proposed device detects analytes with refractive indices ranging from 1.28 to 1.38 with a maximum wavelength sensitivity of 34,000 nm/RIU. The amplitude sensitivity (AS) of the sensor reaches $1026\hspace{0.25em} RIU-1$ with a resolution of $5.55\times 10-6\hspace{0.25em} RIU$ . Our design incorporates a miniature center air hole in the PCF to excite core-guided mode, and reduced air hole diameter along the vertical plane enhances the phase coherence between the plasmonic and the core-guided mode for $y$ -polarized light for a narrow spectrum, ensuring higher FOM and hence greater sensitivity.