I'm at level 56 and now I can't use any weapons, spells or shouts. I can't open any doors or chests, all I can do is run and walk. What can I do?

Try doing something that forces your player character to perform some kind of animation such as sitting down on a chair, chopping wood, mining ore, etc. and maybe this will solve your issue.

Sit down in a chair. Try mining for stone at your house.