You are saying that your work is basically by sitting in front of computer, with fingers as the only body part in movement. This would cause other muscles to get stiffed. When muscles of neck spine are involved, you start experiencing the current symptoms.
I would recommend to get work pauses often associated with light stretching exercises to avoid stiffness
You should check your eyes for any other problem as computer work is also associated with eye disorders.
Check your blood pressure, especially while having such pulsation and record it and pass it to your physician.
Hope it helped!