Achieving significant doping in GaAs/AlAs core/shell nanowires (NWs) is of considerable technological importance but remains a challenge due to the amphoteric behavior of the dopant atoms. Here we show that placing a narrow GaAs quantum well in the AlAs shell effectively getters residual carbon acceptors leading to an unintentional p-type doping. Magneto-optical studies of such a GaAs/AlAs core-multishell NW reveal quantum confined emission. Theoretical calculations of NW electronic structure confirm quantum confinement of carriers at the core/shell interface due to the presence of ionized carbon acceptors in the 1 nm GaAs layer in the shell. Microphotoluminescence in high magnetic field shows a clear signature of avoided crossings of the n = 0 Landau level emission line with the n = 2 Landau level TO phonon replica. The coupling is caused by the resonant hole-phonon interaction, which points to a large two-dimensional hole density in the structure.