Proxima Centauri b, the nearest potentially habitable exoplanet to the Solar System, has likely experienced orbital and rotational evolution due to tidal interaction with its host star and perturbations from its recently-confirmed companion, Proxima Centauri c. A possible barrier to abiogenesis on Proxima b could be that it quickly became a synchronous rotator due to tidal damping of its rotational frequency. To explore this possibility, we used the VPLanet software suite to simulate the system for a 7 Gyr time period and evaluated the limits of its orbital and rotational evolution. As the orbital planes of the two planets are currently unconstrained, we considered a range of mutual inclinations and required other orbital and physical parameters to be within observational uncertainties. We find that Proxima b could have rotated non-synchronously for up to 3 Gyr because perturbations from Proxima c maintained its eccentricity at large enough values to delay capture into the synchronous state. These results suggest that, due to the interplay of tidal dissipation and planet-planet gravitational interactions, Proxima b may have a complex dynamical history that impacts the likelihood of present-day habitability.