I would never deign to "prescribe," but have you given GABA supplementation a try?
A doctor favoring pharmaceuticals might suggest Lyrica (or in the past, its generally inferior cousin Neurontin), but there's another way other than Lyrica or Benzodiazepines to boost GABA levels....it's by taking the amino acid GABA itself.
This is a similar strategy to supplementing the body's natural production of Serotonin and Dopamine by taking 5-HTP and L-Tyrosine (preferably N-Acetyl-L-Tyrosine, a step closer in the metabolic process) respectively, which are precursor aminos to those neurochemicals. Rather than taking pharmaceuticals which prevent the re-uptake of those neurochemicals -- thereby boosting the levels in the spaces between neurons -- supplementation of these amino acids boosts those levels by ensuring that the brain has more raw material to make them with.
This is a more natural process, and doesn't try to circumvent the brain's self-regulatory systems, which always correct any such "artificial" imbalance. This is known as tolerance, dependence and withdrawal. I know all too much about it, having had to take myself on and off of various pain medications over the years and having to wean myself off of many other dependency-causing pharmaceuticals. Some of the least "demonized" prescription medications are among the worst offenders in this area; opiates are far from the only ones or even the worst by far.
More or less the only reason that these pharmaceuticals are prescribed instead of the relevant amino acids are that corporations can't patent a naturally occuring amino acid. So, they can't profit from it to anywhere near the same degree as some random artificially produced molecule. Every case is different, but IMHO supplementation of the problem neurochemical precursor (assuming that levels are really too low, which your case certainly sounds like -- a lack of GABA and possibly other neurochems, perhaps endogenous opiates and cannabinoids) is usually the best overall approach. It comes with little to no dependence, and tolerance is far less of an issue.
Of course it won't fix the underlying cause, but it might be a useful treatment to try. In the case of GABA, your metabolism breaks it down into a precursor which is then metabolized back into GABA inside the brain. This may not boost GABA levels in your neurons as much as 5-HTP boosts your Serotonin or N-Acetyl-L-Tyrosine boosts your Dopamine, it can be effective once you find the right dose.
If you decide to try it, please do let us know how it works (or doesn't) for you. There is no substitute for hands-on experience with things like this, and there's not nearly enough information out there about GABA supplementation. I've heard plenty of people report that it was beneficial, but the more we can all learn about it, the better.
Conditions: Reactive Arthralgia/Reactive Constellation, Chronic Pelvic Pain Syndrome, Sacroiliitis, Costochondritis, widespread Tendonitis, severe back pain & spasms with numerous spinal problems, barely able to type anymore due to severe full-body runaway inflammation, and on and on. Typical daily pain levels exceed 8.5(!)
Medications: Methadone, Dilaudid, Oxycodone, Marinol, Cesamet, Lidocaine Patches, Flexeril, Zanaflex, Soma, Desipramine; many herbs & supplements.
Previous medications: Oxycontin, Opana, Fentanyl patches, Kadian, Avinza, MS Contin, Lortab, OxyIR, Baclofen, Testosterone (oral, patches, gel), Cymbalta, Lyrica, Neurontin, Amitryptyline, every NSAID known to man, Prednisone....and many, MANY more.