Consider how a brace actually trains your body to move differently while injured. It's about preventing the next tweak, not just masking the current one.
Honestly, how bad can it be? I tweaked my back plenty of times working on cars, and it always sorts itself out. A brace seems like a quick fix for what's probably just a muscle pull. Those things are uncomfortable and don't really solve the root problem. Pain is one thing, but calling for a back brace after one incident sounds a bit dramatic. Have you tried just resting it and using some ice? Most of these injuries heal on their own without any fancy gear.