Thank you for your question - certainly an interesting one. Without knowing where exactly the injection was placed it is hard to know what effect you should have experienced.
Nevertheless, steroid injections typically last a few months and allow the individual to do other rehabilitation/treatments for their pain symptoms. The duration of the effects can also depend on
1. The individual
2. Activity levels
3. Previous injections
From clinical experience of facet joint and nerve root injections, the effect is typically seen within within a month, but again it depends on the individual. I usually advised patients to wait for at least 4-6 weeks before passing judgement on the effect of an injection.
If you have concerns, it might be worth speaking to your doctor or seeking an opinion from a Sports/MSK physician or physiotherapist.
I hope this helps.
BW
Dr Dinesh