Because you don't report any other symptoms, such as weakness, numbness or pins and needles in the buttock or legs, it is unlikely that your pain is due to a degenerative disk or joint.
The bleeding associated with either of these will also account for the tenderness.
Sprains and strains are caused by an overload to the area, too-rapid a movement or poor posture and I would ask your GP for an appointment with a physio if it affects your work.
Also try dramatically changing your driving and desk position for a few weeks in order to change the load on your back.
Short of that, our Atrosan® Devils Claw is licensed for back and muscle pain. While it won't help straight away, its effects do increase as time goes on (over a few weeks), unlike most anti-inflammatory medicines.