I'm not receiving sound notifications on either my apple watch or iphone.

The first (and simplest) thing to try if something isn’t working right is to restart your Apple Watch and its paired iPhone. If necessary (device not responding), try a forced restart. Both methods can be found here:

How to restart your Apple Watch - Apple Support

Restart your iPhone - Apple Support

If that doesn't help, the next steps would be to unpair and pair your watch again and restore from the backup just created. This should result in no loss of data. It deletes all temp and corrupted files and re-indexes the file system.

Unpair and erase your Apple Watch - Apple Support

Set up your Apple Watch - Apple Support

Notifications go to either your Apple Watch or iPhone, but not both.  If your iPhone is unlocked, you'll get notifications on your iPhone instead of your Apple Watch. If your iPhone is locked or asleep, you'll get notifications on your Apple Watch, unless your Apple Watch is locked with your passcode. For more info, see:

Notifications on your Apple Watch - Apple Support