i had a spinal injury and it doesn't sound like an acute issue at this time.
We all have some degree of herniation after age 20. it's usually lumbar but a serious lifter could have more issues with the thoracic spine than a regular guy.
Stuart McGill PhD comments on a spinal "hitch" which is excessive mobility at one vertebra than is more than normal.
It sounds more like you have some asymmetry and possible fascial tightness. Usually, that stuff is hard to find on your own and a good massage therapist can help you out. It can often just be tight quadratus lumborum, sprained longissimus, multifidus or something similar...
Sometimes, tightness in an area is the symptom and not the problem. For example, a tight neck or hips or feet/calves will cause compensation movement patterns that will cause your mid back to tighten up as it tries to make up for weakness or reduced ROM somewhere else.
If it's tightness, etc. then you are not in imminent danger, but lifting heavy under those conditions can cause further injury since you could be lifting very heavy with the muscles pulling unevenly. That can tear muscles or herniate discs if the compensating muscles fail during a lift.
Definitely use a good warmup, do some cool down rolling and/or stretching and know when to keep the workout light if you're feeling off.
And, Swede is right, if you have a medical history or it doesn't steadily improve with attention, go see the doc to get ahead of it.