We present full 3-28 μm JWST MIRI/MRS and NIRSpec/IFU spectra of the western nucleus of Arp 220, the nearest ultraluminous infrared galaxy. This nucleus has long been suggested to possibly host an embedded Compton-thick AGN. Millimetre observations of the dust continuum suggest the presence of a distinct 20 pc core with a dust temperature of Td ≳ 500 K, in addition to a 100 pc circumnuclear starburst disc. However, unambiguously identifying the nature of this core is challenging, due to the immense obscuration, the nuclear starburst activity, and the nearby eastern nucleus. With the JWST integral field spectrographs, for the first time we can separate the two nuclei across this full wavelength range, revealing a wealth of molecular absorption features towards the western nucleus. We analysed the rovibrational bands detected at 4-22 μm, deriving column densities and rotational temperatures for ten distinct species. Optically thick features of C2H2, HCN, and HNC suggest that this molecular gas is hidden behind a curtain of cooler dust and indicate that the column densities of C2H2 and HCN are an order of magnitude higher than previously derived from Spitzer observations. We identified a warm HCN component with a rotational temperature of Trot = 330 K, which we associate with radiative excitation by the hot inner nucleus. We propose a geometry where the detected molecular gas is located in the inner regions of the starburst disc, directly surrounding the hot 20 pc core. The chemical footprint of the western nucleus is reminiscent of that of hot cores, with additional evidence of shocks. Despite the molecular material's close proximity to the central source, no evidence for the presence of an AGN in the form of X-ray-driven chemistry or extreme excitation was found.