I was on the muscle relaxant for a full day, and I was no better. Any time I moved, I was retriggering the spasm.
The neck brace stopped that. I still had to be careful, but at least I could walk around and sit and such without constantly re-spasming (which I suspect was actually exacerbating the injury).
I do agree in concept with the concern about combining such an injury / muscle relaxant with strong pain killers. The pain is warning you as to damage; numbing it seems like it might well promote furthering that damage and/or hindering healing.
In my case, once I was braced and stopped retrigging -- and possibly worsening -- the spasming, the remaining pain was entirely tolerable. Of course, the limited effective activity was another aspect requiring coping. That included sleeping: Getting into bed, and keeping things immobilized in bed, was a bit of effort. I learned how to sleep with a neck brace on, and I "trained" myself quickly not to roll from side to side -- despite my allergies that promote frequent shifting.
Had you continued the muscle relaxant (the problem was an involuntary muscle spasm), you possibly could have avoided further treatment (the neck brace).
If I suffer a muscle spasm that can't be massaged out, then a muscle relaxant + ibuprofen serves well for 1-2 days and, after that, only ibuprofen.
IMO muscle relaxants + narcotics is not a useful combination, their purposes(muscle relaxation vs pain-reduction) being orthogonal, except in cases of severe injury where near-immobilization is required.