Should I be wearing a back brace if I have a disc injury?

No I would not recommend a back brace to treat your injured disk.  Back brace can actually make your back more weak leading to more pain.  Back braces are used most often after a spine fracture or fusion surgery to provide extra stability to promote bone healing.   Core strengthening though yoga or other isometric exercises would be better treatment then a back brace.  For more information please contact Executive Spine Surgery.  Good Luck!