I think quite a few have had a variety of injections to calm muscle spasms.
Only a rare few had complications if I recall correctly.

Has the physio person tried trigger point and a variety of muscle/ fascia release styles already?
Does she work on your posture also and give you "homework"?

But from what I have read over the years { and how my chiro explained it}, if the nerve is compressed or having even a twinge of impingement from whatever - be it sticky tissues, muscles, bones or ligaments - the nerve sends a signal to the muscles causing them to react and then the tightened muscle in turn can happen to impinge the nerve or others even more.
Then a bad cycle is created.
And it needs to be broken and the true cause discovered if at all possible.

I don't have any personal experience or input on the injections.

But if you do go ahead with it be sure the Dr is experienced and skilled.

A question for anyone-
For most injections is a fluoroscope? {for visual} recommended for proper placement?