I think a proper biomechanical evaluation is a must in your case. Unless the condition is specifically diagnosed, no advices can be given as such.
It may be a chance of muscle strain injury due to repeated stess, a ligament injury, joint damage (usually facet joint of vertebra or SI joint) etc. Even if a person is fit and healthy, there will chances of muscle imbalance, due to wrong posture, poor biomechanics in games and activities etc, in your case constant sitting and forward movement may have caused repeated microtears in muscle or ligament in the lowerback. Just core exercises alone won't help you, you may need appropriate rest, electromechanical treatment for accelerating the healing process, Therapeutic taping to isotate the area from repeated stress at work and activities etc. If a proper elevatution is done by a well qualified physiotherapist and differentiate the exact cause, then the recovery will be much faster, as there are tailored treatments regimes for each specific conditions.
Next Steps
Consult a good orthopedic /sports physiotherapist and get evaluated. Certain cases second or third opinion is needed to rule out the confusion.
Best wishes
Health Tips
Things to try at home if possible.
Try ice massage (ice cube wraped lighlty in a handkerchief or in a small piece of cloth, ask someone to massage in small circular movement around the area). Icing not only a natural pain reliever, but also helps in accellerating the healing process)
Maintain a good posture always.
Moreover, don't delay, get yourself evaluated properly.