Could you try deleting the App. Then logging out of your iPhone's Apple ID in settings;
Settings > iTunes & App Stores > Apple ID: email@example.com > Sign Out.
Now restart your phone. Once you have done this. Navigate back to the above screen and Log back in with your Apple ID.
Then redownload the Watch app.
Failing this, try logging in with another family member/friends Apple ID and try downloading the app again.
If this doesn't work, then I would suggest doing a factory reset on your iPhone;
Settings > General > Reset > Erase All Content and Settings
Setup as a new phone (not an iCloud Backup as your phone could have been bugged when you backed it up) an try downloading the App. And see if this works. Things such as your Photos and Music will redownload when you log back into your iCloud account.
Last resort, take to Apple and explain what you have already done and see if they can have a stab at it, but this would be my approach first.
Hope this helps.