From your symptom analysis I feel that this could be a radiculopathy or a pinched nerve anywhere along its course.
This usually occurs due to pressure or force on the nerve anywhere along its tract by the adjacent tissues like - bone or tendon or inter-vertebral disc (commonly called a herniated disc). The discs that sit between the vertebrae have a tough outer shell and jelly-like center. The outer shell of the discs can sometimes break open, spilling the jelly material inside. This is what doctors call a herniated disc. Herniated discs can cause symptoms, because the jelly material that spills out of them can irritate nearby nerves. Plus, the disc itself can bulge and press on nerves.
There are tests that can check for a herniated disc, but most people do not need them. That's because many people who have symptoms of a herniated disc get better on their own, regardless of what that test shows.
Imaging tests, such as an MRI or a CT scan, can show what the tissues inside the back look like. These tests can find a herniated disc if one is there. But doctors do not usually offer this test until a person has had symptoms for at least 4 to 6 weeks. In most cases, it does not make sense to order the test sooner, because the treatment for herniated disc during those first few weeks is the same no matter what an imaging test might show.
Management includes -
●Pain medicines that you can get without a prescription. (If these do not work, doctors and nurses can prescribe stronger pain medicines.)
●Medicines to relax the muscles (called muscle relaxants)
●Injections of medicines that numb the back or reduce swelling
●Physical therapy to teach you special exercises and stretches
●Spinal manipulation, which is when someone like a physical therapist or a chiropractor moves or "adjusts" the joints of your back
●Acupuncture, which is when someone who knows traditional Chinese medicine inserts tiny needles into your body to block pain signals
If not better then surgery might be contemplated.