A collision between an interplanetary disturbance in the solar wind and the heliospheric termination shock leads to the generation and propagation of plasma structures in the inner heliosheath (IHS). This interaction can lead to one or more shocks propagating in the IHS until they collide with the heliopause (HP). IHS shocks are (1) partially reflected at the HP and propagate back into the IHS and (2) partially transmitted into the very local interstellar medium. The IHS is dominated by the pressure of energetic particles as was observed by the Low Energy Charged Particle instrument on Voyager 2 and by remote observations from Interstellar Boundary Explorer (IBEX), making the plasma beta, when the energetic particle pressure is included, much greater than one. We model IHS shocks using a pickup ion (PUI)-mediated plasma model and show that they are mediated by PUIs. The dissipation mechanism at perpendicular IHS shocks results primarily in PUIs being heated. Only a very small percentage of the upstream solar wind flow energy is converted to heating of lower energy solar wind ions at the shock. IHS shocks are broad because the diffusion coefficient associated with PUIs is large. The presence of IHS shocks results in greater heating of the PUI component in the IHS. The increased temperature enhances the production of energetic neutral atoms (ENAs) due to charge exchange between IHS PUIs and interstellar neutral gas. When IHS shocks are included in the model, we find that the predicted enhancement of the ENA flux leads to better consistency with corresponding IBEX observations.