Vorticity fluctuations have been identified as an important coupling mechanism during velocity-coupled combustion instability in swirl-stabilized flames. Acoustic oscillations in the combustor can cause all components of vorticity to oscillate, particularly the cross-stream, or azimuthal, vorticity that is excited in shear layer roll-up, and streamwise, or axial, vorticity that is excited during swirl fluctuations. These fluctuations can be induced by longitudinal acoustic fluctuations that oscillate across the swirler and dump plane upstream of the flame. While these fluctuations have been identified in a number of configurations, the sensitivity of this mechanism to flow configuration and boundary conditions has not been studied parametrically. In this study, we investigate the impact of time-averaged swirl level, confinement, and forcing frequency and amplitude on vorticity fluctuation dynamics in the azimuthal direction of a non-reacting swirling jet. The goal of this work is to better understand the dependence of vorticity fluctuations on these parameters as well as the vorticity conversion processes that occur in the flow. We have shown that vorticity fluctuation levels vary with time-averaged swirl number, particularly in the presence of a self-excited precessing vortex core, which dampens most acoustically-driven motion. Additionally, variations in forcing frequency excite flow response in different portions of the flow, particularly for different swirl numbers. Finally, confinement drastically changes the flow topology and unforced dynamics, resulting in significantly different response to forcing and generation of vortical fluctuations.