  We constrain the proper motions of five OB stars associated with candidate
stellar wind bow shocks in the Carina Nebula using HST ACS imaging over 9--10
year baselines. These proper motions allow us to directly compare each star's
motion to the orientation of its candidate bow shock. Although these stars are
saturated in our imaging, we assess their motion by the shifts required to
minimize residuals in their Airy rings. The results limit the direction of each
star's motion to sectors less than 90 degrees wide. None of the five stars are
moving away from the Carina Nebula's central clusters as runaway stars would
be, confirming that a candidate bow shock is not necessarily indicative of a
runaway star. Two of the five stars are moving tangentially relative to the
orientation of their candidate bow shocks, both of which point at the OB
cluster Trumpler 14. In these cases, the large-scale flow of the interstellar
medium, powered by feedback from the cluster, appears to dominate over the
motion of the star in producing the observed candidate bow shock. The remaining
three stars all have some component of motion toward the central clusters,
meaning that we cannot distinguish whether their candidate bow shocks are
indicators of stellar motion, of the flow of ambient gas, or of density
gradients in their surroundings. In addition, these stars' lack of outward
motion hints that the distributed massive-star population in Carina's South
Pillars region formed in place, rather than migrating out from the
association's central clusters.
