Various observations are revealing the widespread occurrence of fast and powerful winds in active galactic nuclei (AGN) that are distinct from relativistic jets, likely launched from accretion disks. Such winds can harbor collisionless shocks at different locations that may induce acceleration of protons and electrons and consequent nonthermal emission. We focus on the inner regions of the winds, where interactions of accelerated protons with the nuclear radiation field and/or ambient gas clouds can induce emission of high-energy neutrinos and gamma rays. In particular, we address the case of NGC 1068, a nearby Seyfert galaxy bearing a prominent wind, which is a known source of GeV gamma rays as well as a tentative source of sub-PeV neutrinos. Considering $p¥gamma$, $pp$, as well as all relevant electromagnetic processes in such regions, we model the multi-messenger emission of NGC 1068. The relatively soft neutrino spectrum indicated by IceCube may favor a predominantly $pp$ interpretation in which high-energy protons interact with gas that has densities typical of broad line region clouds. The accompanying cascade emission modulated by $¥gamma¥gamma$ absorption in the AGN radiation field may account for the observed GeV emission under certain conditions.