When I walk or run I get a very tight feeling in my arch. Does this mean there is something wrong with my arch or my shoes? What can I do about this pain.

The symptom you are describing can have many causes, including problems with the foot itself, or problems with the footwear, or a combination.

If you have tried different shoes, or a substantial arch support insole without benefit then it is time to get checked out. The evaluation is very individual-specific. You should make an appointment with a knowledgeable physician to have the situation evaluated, and I suspect it can be improved if you do that. When you see your provider, be sure to take in with you the shoes that you usually wear, the shoes that you run in, and any shoes that seem to make the problem worse.