You should know that disc problems don't usually cause pain. Sometimes they do, but usually it's muscle pain, not joint pain. There can be pinching of nerves caused by inflammation of muscles or any injured tissue or yeah, sometimes it can be a disc pinching on a nerve. An x-ray probably wouldn't show that, an MRI might, but if in the X-ray everything solid looks just fine it's usually not going to be the disc and so you would only get an MRI if there was a reason to get one. Regular docs really aren't that great at this stuff, you'd usually see an orthopedic surgeon if you really think you have a disc impinging on a nerve. More likely you have poor posture when you use your phone and your computer and you could very well have irritated all kinds of things snapping your head around like that.
You know, my son has a tic currently that affects his neck and moving his head a certain way. He gets a lot of headaches lately. His doctor doesn't know if it is from the movement of his neck muscles so they are tense or if it is his anxiety/depression which is worse right now. He's also 17 years old. You're pretty young and I'm not sure a tic would cause permanent damage. A lot of times muscles that are all attached in the area you describe become tight. Gentle stretching and ibuprofen can help. Have you tried medical massage? It's pretty awesome at working out various things like this. And if all else fails, perhaps an orthopedic doctor can assess you or a neurologist.