Is it just me? I have the latest updates for the iOS and the Destiny app. I've also uninstalled and reinstalled the app. Can't click on anything but News, Forums and below. NVM
I can't guarantee this'll work but I hope you'll give this a try. Go into your profile -> settings ->app and then delete the cache. If this doesn't work at all then there's going into your settings app and then deleting your cache from there. If neither of these worked you might just have to wait it out and see if it gets better.
From the screen you showed click on your name at the top and on the next screen the three bars top right. Then application and delete both cache and database. You won't affect anything in game but the data is corrupted at present so needs clearing.