It sounds like the steroid shot was a one-time thing. That would suggest that having done the good it was intended to do for your back, it is now gone from your system.
If you're concerned about interactions of any medication you get and things out there in the world, always ask your doctor. Covid is too new for a lot to be known, but if your concern is interactions with more prosaic risks such as bacteria, ask the doc.
I think this is one of the few drugs that proved helpful in the treatment of hospitalized covid patients. It is true that in general corticosteroids weaken the immune system and can have a deleterious effect on the beneficial organisms that protect you from bacterial and fugal infections, but I think it's unlikely it would make you more susceptible to covid as it's used for patients who have it. This is an old steroid as well that has effects that are very well known. They can also increase anxiety, as you're basically injecting adrenaline, but again, most don't have this problem when it's injected where you had your injection. I wouldn't really worry too much about it, but it might be of some benefit to take steps to work on your immune system any time you use steroids. This would include taking probiotics and prebiotics and eating well and sleeping well and exercising, etc. And get vaccinated. Peace.
I see that this question has floated around the internet. I found this though which is recent that states it should affect your getting covid. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7454880/ Hope that helps.