Well, whether they give you pain relief or not depends on whether your pain is still sympathetically maintained or independent. There's no way to tell that until you have the first block done. If you get some relief, it's still maintained(SMP). If you get no relief, there would be no use getting any more because it means the pain is independent(SIP).
Here's an article which talks about the 2 main blocks, Lumbar and SGB. Yours would be sgb, stellate ganglion. It tells what to expect. :-)
Sympathetic Nerve Blocks: A Guide for the Patient.
Hope that helps and I wish you lots of luck and hope this gets you into remission!
Big Hugs,
Karen