With the given details, it's possibly myofascial pain caused due to bad posture often in sitting. The shoulder blade may be pulled forward and downward which stretches the muscles as well as the tight fascia which causes dull aching pain. Stretching of the peripheral nerves in this position may be causing the numbness. Myofascial release techniques by a skilled Physiotherapist can help to relieve the pain. Your Physiotherapist will also advise you on proper sitting posture and scapular conditioning exercises which help in preventing recurrence in future.
Health Tips
Ice packs over the shoulder blade area followed by a warm shower can help. Also try rolling a hard rubber ball over the back squeezing it against the wall in standing position. With arms close to your body try squeezing shoulder blades and holding for 10 seconds and then releasing.