I have a wisdom tooth that has broken and it is causing pain in my shoulder and neck... is it infection or swelling? how severe is this?

How severe: Forget about infection and swelling! You must make a Dentist's appointment as soon as possible. When you contact the dentist tell him or her what the problem is and you will almost certainly be seen on that day or the next. Hope all goes well!

Both: Infection causes swelling. Broken tooth infected. Infection is spreading through your body. From your symptoms I would say very severe. You need immediate dental treatment. This can't be cured with just a pill, or by waiting, or by ignoring it, or by a Physician. See Dentist immediately.