Although all-dielectric sensors exhibit minimal absorption and a high figure of merit (FOM), their sensitivity is significantly lower compared to plasmonic sensors. One approach to enhancing the sensitivity of dielectric sensors is to utilize bound states in the continuum (BICs), which are resonant states with an infinite radiative lifetime. These states are characterized by polarization vortices in the far field, whose winding number determines the topological charge. Here, we demonstrate that the position of a BIC polarization vortex in the k-space has a square-root dependence on changes in the refractive index of the medium, similar to an exceptional point. We compute the angular and spectral sensitivities of our structure and demonstrate that the angular sensitivity reaches values comparable to those of surface plasmon polariton (SPP)-based sensors. We observe a blue spectral shift of BICs as the refractive index of the surrounding medium increases. This behavior differs from the conventional spectral response typically expected under such perturbations. Additionally, we find a distinct BIC regime exhibiting a pronounced angular sensitivity, surpassing its spectral one. Our findings pave the way for the development of dielectric sensors with high angular sensitivity and facilitate the practical observation of the optical vortex dynamics.