Very metal-poor stars are important tracers of the early chemical evolution history of the Milky Way. Infrared H-band spectroscopic surveys, such as APOGEE, are less affected by extinction in the more dust-obscured environments of our Galaxy. However, H-band spectra contain very limited spectral information for stars at the most metal-poor tail ([Fe/H]<-2.5) due to the weakness of available Fe lines in FGK stars in this wavelength range. The first paper in this series successfully identified a sample of 327 very metal-poor stars (with [Fe/H]<-2) from the APOGEE database, out of which 289 stars are on the red giant branch. These spectra were not properly analysed by the APOGEE main pipeline due to their very metal-poor nature. In this work, we measure metallicities for these stars, using the abundances of the elements Mg and Si. We demonstrate that the elements Mg and Si have good quality absorption lines despite the challenging combination of (low) metallicity, wavelength regime, spectral resolution, and signal-to-noise ratios available for these spectra. A specialized pipeline is designed to measure the abundance of Mg and Si in APOGEE spectra, which yields a robust estimate of the overall metallicity. In order to provide reliable measurements, we test 3 different sets of assumptions for Mg and Si enhancement. We present Mg and Si abundances as well as overall metallicities for 327 stars, all of which had previously gotten null values from the main APOGEE pipeline for either the calibrated [M/H] or [Fe/H]. Typical uncertainties for our measurements are 0.2dex. We find in our sample 5 stars with unusually high Si/Mg abundances above 0.5, a signature we connect to globular cluster stars, and that might be related to specific supernova events. Our data suggest a concentration of high Si/Mg stars in the Sextans dwarf galaxy. Other dwarf galaxies are found to be in good agreement with results found in the literature. Our derived metallicities range between -3.1<=[M/H]<=-2.25, thereby pushing the metal-poor tail of APOGEE results down by 0.6dex.