Resonant Raman spectroscopy is realized on closely spaced nanowire-based quantum wells. Phonon quantization consistent with 2.4-nm-thick quantum wells is observed, in agreement with cross-section transmission electron microscopy measurements and photoluminescence experiments. The creation of a high-density plasma within the quantized structures is demonstrated by the observation of coupled plasmon-phonon modes. The density of the plasma and thereby the plasmon-phonon interaction is controlled with the excitation power. This work represents a base for further studies on confined high-density charge systems in nanowires.