In superconductors the Anderson-Higgs mechanism allows for the existence of a collective amplitude (Higgs) mode which can couple to eV light mainly in a nonlinear Raman-like process. The experimental nonequilibrium results on isotropic superconductors have been explained going beyond the BCS theory including the Higgs mode. Furthermore, in anisotropic d-wave superconductors strong interaction effects with other modes are expected. Here we calculate the Raman contribution of the Higgs mode from a new perspective, including many-body Higgs oscillations effects and their consequences in conventional, spontaneous Raman spectroscopy. Our results suggest a significant contribution to the intensity of the A_{1g} symmetry Raman spectrum in d-wave superconductors. In order to test our theory, we predict the presence of measurable characteristic oscillations in THz quench-optical probe time-dependent reflectivity experiments.