Recent tunneling measurements on infinite-layer nickelates have revealed spatially varying superconducting symmetries, whose microscopic origin remains unclear. Motivated by this observation, we investigate the interplay between electron correlations and electron-phonon interactions in infinite-layer nickelates by combining first-principles calculations with the fluctuation-exchange-Migdal-Eliashberg theory. Our calculations show that spin fluctuations yield robust d-wave superconductivity on the Ni d_(x²-y²) orbital, whereas electron-phonon coupling induces s-wave pairing on an interstitial orbital, leading to an s+id superconducting state. The emergence of the s-wave component is strongly carrier-density dependent: an intermediate electron-phonon coupling of λ=0.4 stabilizes the s+id state at n=0.9 but not at n=0.8. These results imply that local oxygen defects tune the local electron density and form finite-size domains with distinct pairing symmetries, offering a compelling explanation for the spatially inhomogeneous superconducting symmetries observed in experiments.