The two are definitely related. Changing the orientation could help, but then maybe you would have the same issue in another area. Being aware of the fact that your head orientation does affect the musculature in your neck is a good star to finding a solution.
I am a big fan of regular massage. While massage will alleviate some issues, daily stretching is the thing that will keep these pains from developing into a chronic problem. There are lots of good neck stretches that you can do while sitting in your chair.
Grip the bottom of the chair with the left hand. Reach over your head with your right hand and place it on your left ear. With your neck in neutral position, pull your right eat down toward your right shoulder. Hold for 2 to 3 seconds, release and return to neutral. Repeat several times then duplicate on the opposite side.
Next turn your face 45 degrees to the right, and reach your right hand up and place it on the back of your head close to your neck. Pull your nose down toward your right pec. Hold for 2 to 3 seconds, release and return to neutral. Repeat several times then duplicate on the opposite side.
For the last stretch, turn your face 45 degrees to the left, and reach over your head with your right hand, and place it on your left ear. Pull your right ear down toward your right pec. Hold for 2 to 3 seconds, release and return to neutral. Repeat several times then duplicate on the opposite side.
You can do these stretches several times a day, but don't stop doing them just because it feels better. Unless you change your work conditions, you should probably continue to do these on a daily basis.
If these stretches do not alleviate the pain you're experiencing, I would suggest you consider seeing a physical therapist to address a possible underlying problem.