I hurt my back about a year ago falling down the stairs. Different injury as it wasn't related to lifting. (Before I fell down the stairs I was deadlifting greater than double my body weight). I didn't wait long enough to fully recover and got back into the gym to early. I also tried to pick up from where I left off before the injury and ended up straining my back even more.
Acupuncture helped me almost immediately. In addition, I've been doing physical therapy for the last 2 months. Half way through I noticed immediate improvements. It was a combination of stretches, massage, and simple exercises that helped rebuild injured muscles. I'm slowly making my way back into the gym now and am feeling pretty good again. As I got to chat with the therapist, many of the back injuries she said she sees are related to weak backs rather than trauma, like my case.
I'm not an expert or doctor, but this sounds like a case of a weak back to me. Time will heal your back; however, without proper exercise and strength training, your muscles will continue to atrophy. You will be likely to hurt yourself again and require regularly seeing a chiropractor/acupuncturist.
Physical therapy can be particularly useful as they can help assess where you are weak and provide exercises and stretches to strengthen yourself. As you recover and get stronger, you should start doing exercises like backsquats and deadlifts (under proper supervision!) to build stronger muscles in your back, legs and core. This will help prevent future injuries.