Have you been to an orthopedist or just your primary? You can get X-rays but they won't show nerve issues. Would need an MRI for that. Assuming you aren't having any deficits indicative of nerve involvement (numbness, tingling, burning pains that shoot somewhere else) or they would have done one right away to CYA. If it is a muscular strain a chiro won't do anything, as you stated. Unfortunately muscular injuries are a b* to heal, esp neck/back inj. The biggest thing is to let them rest and then rebuild them properly. Over an awful long period of time, be patient. :( Posture and leg/ab muscles are your key players there.. If your core is weak, your back has to compensate. Lumbar injury is so common because there's no support (rib cage) to further stabilize when having to compensate or twist/turn. Once you've hurt it, you're much more susceptible to re-injury..
If you haven't been to an orthopedist, go see one. Or if you have, go back! Living that way is miserable, please don't settle. Get into physical therapy if they think it's a good option for you. Ask about massage and ultrasound therapy too. Muscle relaxers with NSAID (ibuprofen, Tylenol, aleve- whatever works best for you) can help short term for pain to rebuild and then be kept handy for bad days if your ortho thinks it's a good option for you.
It's a vicious cycle if left alone. The muscle tension is effecting the nerves, which can permanently damage them and cause chronic pain. The pain will be miserable, and heavy NSAID/pain med use trying to manage it will demolish your liver.