Hey Tina and WELCOME=)
Just some thoughts...If it were me, I would cancel that long drive. That distance is hard on anyone's body, especially with spinal issues. Secondly, as previous post suggested, the injection will cause discomfort at first. Agreed that you should plan to take the afternoon off and allow your body to relax. No, to answer your question...relief will not come instantly, if it comes at all. Results and degrees of relief post-injection varies from one patient to the next. I hope that you will have success with yours.
I can only speak from my personal experience. I have attempted several different series of epidural injections over the years for both cervical and lumbar pain. I did not get relief, with ANY of the injections. The cervical ones actually made my spine even more "angry".
Meanwhile, have you ever tried Skelaxin or Soma? IMO I would try one of those before enduring the injections.
Hugs~~Dixie