Corticosteroid shots are known to have gastrointestinal reflux or heartburn as a possible side effect. Smoking should not have any effect on whether the heartburn occurs as a side effect, only the way your body reacts to the injection.
A steroid shot is unlikely to causes symptoms such as heartburn regardless of whether or not you smoke. However, smoking in and off it self can be associated with esophageal problems and symptoms.
My Mom gets corticosteroid shots every 3 months and she also smokes. She has no trouble with heartburn. I'd watch what foods cause the burn and avoid those.
It is very unlikely that a corticosteroid shot has given you heartburn. The reason you have the heartburn is almost certainly directly related to the fact that you do smoke.
Corticosteroids have numerous side effects, one of them being stomach ulcers. However, shortly after an injection, the heartburn probably has other causes and is non-smoking related
