The Starr rehab protocol is thought to be good for muscle belly tears, which your back tweak most likely is not (unless you have a huge bruise near where it hurts). I don't really know what back tweaks are, but they don't show up on x-ray, so that will probably not be a helpful test, and will just give your doctor an opportunity to tell you that you have arthritis in your back, or loss of disc height, and maybe you shouldn't lift heavy things. If so, he or she will be wrong about that.
The general recommendation is to drop down to a weight where you can do the movement without limiting pain, and basically work your way up gradually from there. Will M or others may have more detailed suggestions.
I have trained through a number of back tweaks this way. They suck, but over the past two years since I started lifting and following SS more or less, they (tweaks) have become much more rare and brief with this approach.