Well, the main treatment for disc herniation and radiculopathy is surgery and conservative treatment (e.g., injection etc). Surgery is generally for those who don't respond to injection treatment.
I am not sure why all the three doctors you've seen just only recommended injection instead of surgery. Maybe you should see an orthopedic surgeon for this. If you've seen a surgeon and still got injection only, then the reason may be that you are not a good candidate for surgery and conservative treatment is the best option.