The injections would not fix the cause of the sciatica but physical therapy might.
I have this because I have disc problems, 3 disc repair surgeries and currently a bulging disc,
The physical thereapy helped a great deal as does sleeping in a position that does not irritate and supporting my back when I sit, etc.
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Hi Joseph. It is important to understand that "sciatica" is a general term that lacks diagnostic specificity – that is, it says nothing about the CAUSE of the neurological pain.

First, a proper diagnosis should determine the CAUSE of the sciatic type of pain.

Second, specific treatment should target correcting or mitigating that cause.

Chiropractors are specialists in diagnosing and treating these types of problems. It might be wise to have a thorough evaluation by your family Chiropractor.

Best wishes and good luck.
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Try inversion therapy (hanging upside down).
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Research demonstrates that overall, most people who have injections are no better off a week or two later. However, in people whose symptoms persisted even with physical therapy, therapy often becomes more effective once an injection has been administered. This is especially true for those whose symptoms are constant and radiate all the way to the foot.

Physical therapy is an excellent choice. While it’s true that the term "sciatica" is often misappropriately applied, it is NOT true that you HAVE to know the exact source of the sysmptoms before it is treated. Rather, research demonstrates that sciatica (whether a true "radiculopathy" or a referred "somatic" pain from the intervertebral disc, or sacroiliac joint, or hip), or any musculoskeletal pain can be treated without expensive imagining or ever knowing the true pathoanatomic cause of the symptoms. It remains unknown in 85% of cases anyway.

Rather, assessment and treatment by LISTENING to YOUR history and observing what happens to the symptoms when you move is demonstrated to be a reliable and valid way to direct treatment…all by showing you how you can fix it yourself with very little intervention from a clinician. This approach to treating it is prevalant by physical therapist and chiropractors who are certified in Mechanical Diagnosis and Therapy (www.mckenziemdt.org). I would recommend you locate a practicioner who is certified in this.
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I am a PT