This happens to me. My lower back feels fine most of the time, but flares up with pain when I sneeze (especially while sitting), or mis-step. Running can also aggravate it. It's also sore when I first get out of bed.
Currently, I get acupuncture on it and do exercises at the gym, but am open to hearing more.
Please take the following as the anecdote it is. I am not a medical professional, but I'm happy to share my experience.
As I previously mentioned, I suffered significant chronic and acute for quite some time, and it reached a point where my quality of life was affected. During the course of my suffering, I investigated all sorts of avenues for pain relief, such as seeing a GP, Physio, Chiro, Osteo, Physiologist. I did Yoga, went to gym 3 to 4 times a week, took anti inflammatories and started smoking weed. None of these did anything apart from anti inflammatories occasionally (i.e: took them all the time, and sometimes they made my back pain bearable). This was the only way I could surf, but it meant that I went through boxes of the sh!t a month and it was causing havoc on my stomach / could sh!t through a straw.
I finally decided to visit a Neurosurgeon. We discussed the causes of back pain, where he drew a Venn diagram and explained the different sources of back pain. His speciality, being the "bone" part that could cause the pain. He described some symptoms that is a result of degenerative disk disease (
https://www.spine-health.com/conditions/degenerative-disc-disease/what-degenerative-disc-disease), which is basically the narrowing of the space between your vertabrea. This big indicator here, for me, was the symptoms I have mentioned / you've quoted. Sneezing in bed for me was like a little death sentence every time it happened ( I have hayfever, so it happens a lot!).
Even though my symptoms were "severe", the diagnosis by the neurosurgeon was never cut and dry, even after an MRI and a contrast injected bone scan (
on the plus side, the contrast injected is nuclear medicine, and I'm pretty sure I can shoot spiderwebs out of my palms now). The Neuro suggested that I do a Discography (
https://en.wikipedia.org/wiki/Lumbar_provocative_discography ) to which I said "fuuuuuuck thaaaaat" ( I'm a bit of a nervous patient and that procedure was a step too far...you need to be aware while they drill your spine with needles to simulate disk pain!). After the above diagnostic steps were taken / avoided, I was left with a choice; live with the pain and find some other avenue for pain relief, or get a disk removed and fuse the L5/S1 vertebrae.
I have hurt myself a lot in my life, mostly because I took up downhill mountain bike racing, so I've torn muscles, ligaments, broke arm, broke shoulder, dislocated shoulder and countless sprains / loss of skin and blood. I mentioned this, because I know what different kind of pain feels like.
My "gut feel" for what the source of the pain is, coupled with the symptoms, convinced me to YOLO a ALIF surgery (
https://www.spine-health.com/treatment/spinal-fusion/anterior-lumbar-interbody-fusion-alif-surgery) . They make a cut above your pepe from the front, move your guts to the side, chip out a disk and bolt that sh!t down with titanium bits. This has been one of the best decisions of my life, as I'm sat here, 5 months later with no back pain anymore, havent had a pain killer since 2 weeks after the operation and I'm back to surfing awfully.
Your case might not be as severe as mine was, so you might* benefit from trying inversion tables, which aims to decompress your spine, by stretching out the spacing between your vertebrae.