I occasionally get something similar and find that both my neck and one shoulder is agonizing.
The physio got me to do some exercises to relieve them with some basic stretching and this keeps it under control. Here are some exercises for posture improvement as well, I totally forgot to mention them.
I use a treadmill but you can do this on walks. 20 to 25 minutes on the treadmill as fast as I can without straining. I try to stand up very straight with my shoulders relaxed, my arms naturally swinging and my abdomen slightly tight. Pull in your chin so your ears over your shoulders. Office posture weakens the muscles in your upper back and the back of your neck so this will be hard at first. Chest stretches are also very, very important to help with posture.
I do other exercises for my lower back as well, but this should get you started. And I also sleep on an orthopedic pillow (it’s Uttu, for shoulder pain mostly). It does wonders for me (and my neck).
As with any exercise you undertake, take it slow, gradually build up, if it hurts then you are overdoing the exercise or that exercise it not suitable for your condition, if in doubt ask your physio before attempting any exercise, last outcome you would want to see is it causing more pain.