I had requested a picture of the rash and have not received one.
There are several common rashes to consider in this situation. The injection and oral steroids are oriented towards inflammatory rashes, so the limited response to the steroids would suggest that other causes should be considered.
A major exception that would explain why an inflammatory rash does not resolve with steroids would be if the inflammation is due to an allergy to a substance to which you are still being exposed. When there is ongoing exposure to a substance to which you are allergic, then steroids will frequently only have little or no effect
It is possible that the rash is related to an infection, but there are many different infectious rashes. It is fairly common to develop a rash with common generic viral infections, called a viral exanthem. There are also bacterial infections that are associated with rashes. Trying to identify whether the rash is related to infection, though, would require a review of a picture.
At this point, it would be appropriate to review whether there are any substances to which you are having ongoing exposure. If there is a potential substance that is suspected, it may help to eliminate exposure to that substance. Another option would be to see your doctor again or a Dermatologist.
If you would like to review a picture or if I can provide any additional information, please let me know.