Self-assembling polymers have become an important component of armor materials and protective coatings due to their ability to absorb and dissipate shock energy and rapidly self-seal punctures caused by projectiles. Optimal self-sealing polymers must be both elastically resilient and have fast molecular diffusion during ballistic impact. However, most research on self-assembling polymers has focused on quiescent conditions and relatively little is known about their molecular dynamics in extreme conditions. Here we apply molecular dynamics simulations to model the nanostructure evolution, chain dynamics, and mechanics of model self-assembling elastomers during ballistic impact and interfacial welding. We systematically vary polymer molecular architecture to produce model samples with a variety of self-assembled nanostructures and thermomechanical properties. We then measure how these properties vary as samples undergo shock loading. This enables us to relate the nonequilibrium mechanical resilience and chain dynamics to the underlying molecular architecture, which we use to develop molecular design strategies for improving self-sealing polymers.