Following the recent success of realizing exciton-polariton condensates in cavities, we examine the hybridization of cavity photons with the closest analog of excitons within a superconductor, states called Bardasis-Schrieffer modes. Although these modes do not typically couple linearly to light, one can engineer a coupling with an externally imposed supercurrent, leading to the formation of hybridized Bardasis-Schrieffer-polariton states, which we obtain both as poles of the bosonic Green's function and through the derivation of an effective Hamiltonian picture for the model. These new excitations have nontrivial overlap with both the original photon states and d-wave superconducting fluctuations. We conjecture that a phase-coherent density of these objects could produce a finite d-wave component of the superconducting order parameter---an s{\textpm}id superconducting state.