We present magneto-Raman spectroscopy measurements on suspended graphene to investigate the charge carrier density-dependent electron-electron interaction in the presence of Landau levels. Utilizing gate-tunable magneto-phonon resonances, we extract the charge carrier density dependence of the Landau level transition energies and the associated effective Fermi velocity $v_mathrm{F}$. In contrast to the logarithmic divergence of $v_mathrm{F}$ at zero magnetic field, we find a piecewise linear scaling of $v_mathrm{F}$ as a function of charge carrier density, due to a magnetic field-induced suppression of the long-range Coulomb interaction. We quantitatively confirm our experimental findings by performing tight-binding calculations on the level of the Hartree-Fock approximation, which also allow us to estimate an excitonic binding energy of $approx$ 6 meV contained in the experimentally extracted Landau level transitions energies.
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