Get done ENT consultation and get you throat and neck examined.
There can be any throat infection
because of what there is pain . and it will increase on physical activity as the muscles stretch up and start paining.
You may have to take antibiotics ,decongestant tablets ,gargles if required .
Do not press on your neck this is not going to give relief in any way.
Avoid physical exercises for some time.
Take care of reflux disease.