Hello, the pain you are experiencing is more of mechanical ache. The pain comes from over use of muscles or faulty use i.e. wrong posture. You have to start changing your neck and shoulder postures as often as possible, I'll recommend 'dynamic posture'. Take micro breaks for 5-7seconds every 20 minutes, during which do simple neck movements.
Next Steps
For pain use heat packs for 10min a day for 2-3 days. In case if it is not reducing with heat and postural changes you may need electrotherapy sessions to reduce muscle pain.
After the muscle pain reduces you need to start with neck and shoulder strengthening exercises for improving your muscle endurance as you need to continue with same work, you can learn them from Physiotherapist , specific to muscle weakness you have.
Health Tips
Keep your monitor at your eye level