In this paper, the simultaneous switching and sensing capabilities of a compact plasmonic structure based on a conventional rectangular hole in a silver film are proposed and investigated. The proposed structure has ultrahigh sensitivity up to 3000 nm/RIU and high figure of merit of 170 RIU−1. Also, the simulation results show the potential of the presented refractive index sensor to detect malaria infection, cancer cells, bacillus bacteria, and solution of glucose in water. Simultaneously, by changing the incident lightwave polarization, the structure behaves like a plasmonic switch, which has high extinction ratios of 15.81, 31.20, and 25.03 dB at three telecommunication wavelengths of 850, 1310, and 1550 nm, respectively. The ultrafast response time of 20 fs is achieved for the wideband application of the switching capability at the wavelength range of 1056 to 1765 nm. Moreover, the equivalent circuit model and transmission (ABCD) matrix methods are derived to validate the simulated results. Simple design, good agreement between the numerical and analytical results, biomedical applications, ultrahigh sensitivity, and ultrafast performance of the proposed structure help this idea to open up paths for design and implementation of other multi-application plasmonic devices in near-infrared region. To the best of our knowledge, the mentioned analytical methods have not been studied former at near-infrared wavelengths. Therefore, the achievements could pave the way for verifying the simulation results of plasmonic nanostructures in future investigations.