It's possible, but the symptoms seem different than the injuries I've had before. The pain seems "deeper" and closer to the spine, the healing has been MUCH slower, and it doesn't feel/heal better from getting lots of blood to pump through it from light exercises/stretches. A herniated or bulging disc is my guess, though I'm obviously no expert on this and could be way off. Only odd thing is that the pain is on both sides of the back, more or less evenly.
Well, there is a lot of depth of musculature, especially on the lumbar spine. You have things like the lats and traps that run most of the spine that are superficial. Then you have the nine muscles of the back extensor group. Then you have deep, deep muscle groups like the transversospinal muscles, rotatores, multifidi, semispinalis, spinalis, etc.
It could also be caused by the capsule(s) surrounding the facet joints of the vertebrae. If you are hypermobile at that segment into flexion, then one segment may move too much, causing pain and instability.
It could also be disc pain, but that typically increases with anything that increases intraabdominal pressure and certain postures - coughing, doing a crunch, slumped sitting, bending downward, using the Valsalva, etc.
Continue doing light exercises to help with blood flow, but don't continue an exercise if it elicits your symptoms. You have to let your symptoms be your guide - if you keep flaring yourself up over and over, then the inflammation may become longer lasting, prolonging the injury time.
Do you do much along the lines of core rotation? That may help you activate the deeper muscles better (as they are the main rotators within the spine). You could do that by getting on a hyperextension machine (like the one that follows) and doing rotation exercises back and forth. Also, with that, do you notice that you can rotate more one way than the other? Does it reproduce your pain? If it doesn't hurt, do it for 15-20 reps for a few sets. As you start to feel better, you can start to lean further and further over it to increase the difficulty. Make sure you maintain a neutral spine with normal lordosis throughout (don't go into hyperextension of your spine, which most people do when they get tired).