High-pressure, variable temperature infrared spectroscopy and first-principles calculations on the methane filled ice structure (MH-III) at high pressures are used to investigate the vibrational dynamics related to pressure induced modifications in hydrogen bonding. Infrared spectroscopy of isotopically dilute solutions of H(2)O in D(2)O is employed together with first-principles calculations to characterize proton dynamics with the pressure induced shortening of hydrogen bonds. A Fermi resonance is identified and shown to dominate the infrared spectrum in the pressure region between 10 and 30 GPa. Significant differences in the effects of the Fermi resonance observed between 10 and 300 K arise from the double-well potential energy surface of the hydrogen bond and quantum effects associated with the proton dynamics.