Steroid injections for rotator cuff syndrome are sometimes given, but the official advice suggests the relief may only be short-term.
It's the physio that will make the difference - but steroid injections may make doing the excercises more possible when pain would otherwise prevent you doing them.
If you do get injections, do your physio as well!
Strengthening the muscles really does help the joint return to normal, and non-painful.
I've had frozen shoulder, bad shoulders are the awkwardest things to lie on, particularly if you're a side-sleeper. I used to prop my upper arm up with special pillows.