Only talking from a personal viewpoint here, not a medical one. I have been taking steroids for over 30 years continuously.
No, I am sure that the weight gain isn't anything to do with the injection. At least not just one injection. More than about 3 per year are frowned upon because they can have some side effects and maybe could cause some weight gain, but definitely I would not say after one injection. Also the usual thing to happen is that weight gain usually occurs when taking larger oral doses over a longish period of time.
Perhaps as you are having spinal problems, inactivity might be a part of it ? It's difficult isn't it to even move never mind walk about when your spine is hurting so much.
Hope this helps.