Yes ive tried that - but that's about as technical as I get!
Let's try this and see if we can get your app working properly again. From your Fire Stick Home Screen, go to Settings > Applications > Manage Installed Applications > Amazon Music then select Clear Cache. I would restart the Fire Stick as well after clearing the cache, and see if Amazon Music is working properly again.
If that does not help, let us know exactly what the error message says and we'll help further :)