Take the drugs.
I've battled back issues since I was a kid. Sometimes the muscle relaxers are less about reducing the pain and much more about loosening things up so that everything can get realigned and back into "normal" mode. The first step to that is to stop the muscles from spasming. Sometimes (often) even when that happens, initially, the pain remains because the muscles are so "traumatized" from being in constant spasm. Usually my doc gives me the muscle relaxer AND something for the pain (rather than an "all in one").
My doc ends up giving me Flexeril during every major flair up, coupled with Perscription Strength Tylenol. He could go stronger on the pain meds, but I'm uber sensitive to opiates/narcotics...they basically make me unable to function/work/do anything but sleep.
For the minor ones...he recommends Alleve, rather than Ibuprofen. He starts me at 4 over the counter strength pills a day (2 every 12 hours). Says the Alleve is gentler on the stomach, less of an anti-coagulant, and has less health risks (which, to be clear, are super low %).
Back issues suck. My major ones inevitably lead to a battle with sciatica that can last months. I ended up in PT for 4 months earlier this year because I lifted my youngest up to look at a toy on a shelf at Toys R Us. About 3 months ago I had a minor flare up from COUGHING.
Hope you feel better, soon!