Cavitation occurs in a variety of applications ranging from naval structures to biomedical ultrasound. One important consequence of cavitation is structural damage to neighboring surfaces following repeated inertial collapse of vapor bubbles. Although the mechanical loading produced by the collapse of a single bubble has been widely investigated, less is known about how the presence of a second bubble affects the loading. In such a problem, the bubble-bubble interactions modify the dynamics, e.g., by increasing the non-sphericity of the bubbles and amplifying/hindering the collapse intensity depending on the flow parameters. Here, we quantify the effects of bubble-bubble interactions on the bubble dynamics, as well as the pressures produced by the collapse of a bubble pair near a rigid surface. We perform high-resolution simulations of this problem by solving the three-dimensional compressible Navier-Stokes equations for gas/liquid flows. The results are used to investigate the non-spherical bubble dynamics and characterize the pressure fields based on the relevant parameters entering the problem: stand-off distance from the wall surface, the angle, and the distance between the two bubbles.