You had a nice effect from the local anesthesia, but the steroid has not had time to kick in yet. Keep it iced for the first 2 days, and don't do too much. Walking is for later in my experience. It can take a week for the injection to help, but you usually know if they got the right spot within 3 - 4 days. These things are rarely permanent, but my first one, an epidural at L5/S1 lasted most of a year. I thought they were pretty much always done under fluroscopy nowdays, as standard care.
I have not had much luck with facet joint injections. My last injection was a caudal, right in the tailbone, and it stopped pain in my legs and the lowest part of my back immediately. It's lasting so far, but I'm only a few weeks out. I still have a few zinger needle-like stabs in the feet, but nothing like before! Caudal is supposed to be the easiest to do, hits a bunch of nerves that run down into the legs and feet. It hurts right at the tip of the spine for a week, but seems so far to get rid of the horrible pain. An ice bag with padding is very helpful. You can get good ones that can go right next to the skin and hold about
a quart from a medical supply or ask your pharmacist to order one.
I had muscle spasms right next to the spine that were injected with amazing results also. I didn't think it would work, but it broke the cycle and allowed me to stop diazepam (which is a great muscle relaxant).