Each person is different in this situation. I've had the injections myself. From what I understand the first day or two days can be painful because of the injections. Since the steriod must have time in order to work itself into your system that is another factor in the matter.
In my case, I've had the epidural, the bi-lateral, and the facet joint injections. None of which have worked due to how damaged my back is. The last injection that was performed on me was through the local hospital as an outpatient to test for an ablation (nerve burn) which the doctor decided it wasn't a good idea; now I'm scheduled for a consult with 2 different back surgeons. Note - this has been going on for a yr and a 1/2 with me.. not a fun issue but anyway.
Back to what I was saying about these injections however. The size of the needles are larger (at least I think they are) than your normal needle because of where they are being used and how they have to be used. Something I had done after each injection when I went home was to apply a small ice pack to the area for no longer than 10 minutes; just enough to take away the pain. If you have a muscle relaxer (I take Flexeril) it wouldn't hurt to eat something first then take one before you lay down with your ice pack.
Between the two of those things, you should start feeling an ease of pain. If you have any redness or bruising showing up in the area where the injections were call the doctor asap.. call doctor's office asap.
The doctor who has been giving me the injections had said that I could use ice for the first 12 hours.. 10 minutes on at least an hour to an hour and 1/2 off because you don't want to get frost bite. I went with 15 minutes because I needed the numbness due to the intense pain. You have to judge your own pain level with the ice.
As you start feeling better with the steriod working, you can also try heat instead to see how that works. The heat will help increase the oxygen flow into the area that is hurting. If you can handle some pressure, a warm shower and letting the water roll down your back can help as well but don't let it hit that area.. big time pain!!! I did it one time and oh boy.. never again!!
Anyway. That's about all I can think of for what I went through in taking the small steps of recovery. I hope it all works out for you and best of luck on getting better!