Should I trust my hitch?

Take your vehicle to a reputable body shop and have it inspected!!! Really, I made this same mistake some years back and assumed everything was fine (after a much-lower-speed collision than yours), only to find later on that the place where the receiver bolted onto the frame had been damaged. The rearmost mount points were ruined... the piece they bolted to eventually broke off from the rest of the frame! I ended up having a welding shop fix it. They welded two steel straps that ran from the back of the receiver to the frame sides so the assembly was reinforced, made stronger than original. My point is, let the experts at the body shop make sure all is truly ok before you sign off on the insurance settlement.