I can say with confidence that I am pretty experienced on low back soft tissue injury through experience.
I tore soft tissue in my back and went on a year long marathon of reinjury until I finally figured out how to rehab it and come back strong.
This is what I suggest you do.
1.) Consider seeing a good chiro to make sure your pelvis or lower lumbar spine region isn’t subluxed which may have caused the problem or may be an after effect from the problem.
2.) Take a week off and begin supplementing with fish oil like it’s going out of style if you aren’t already.
3.) Now begin to focus on having incredibly strong core muscles. I suggest beginning core planks (start with the right oblique (on your side) for 30 seconds then roll to the push up position on your elbows with no rest for 30 seconds then to the left oblique, repeat for a total of 3 sets of 30 seconds, build this up over time to 60second reps w/ someone placing a weighted plate on you), do these three times a week.
Then in the future when you go to squat and deadlift, mimic the feeling of your planks in your lift. The cores should be like a fucking brick wall when you move that heavy iron.
4.) Once the acute phase is over (no more pain) begin light stretching. Stretch your hamstrings, hip flexors, glutes, lumbar and hamstrings again. Incorporate this into your routine, it’s nice to do right after your planks. DON’T SLACK ON THIS!
5.) Add dynamic ab work back in but KEEP YOUR PLANKS.
6.) Start deadlifting and squatting again starting with the bar but progress using 10-20lbs additions per week until you eventually get back to where you were. (Let the back PAIN go completely away before loaded training again which will be 1-2 weeks.) I suggest you really analyze your technique and make sure there is absolutely no lumbar flexion going on, ever, you should be arching your whole back so hard that you’re sore the next day, goes for squat and deads (eventually you will learn to keep the lumbar arch while letting the upper back curve on your deads).
7.) After the 1-2 week acute phase start to foam roll the sensitive area on your low back routinely until it is not a sensitive area anymore.
I’m not a strength coach, nor hold any professional title in the field but do compete competitively and this is what has worked for me in the past.