You're in Phone Only, meaning your contacts are not entered to your Google synced account. Go to phone settings. Tap the '+' sign to add a contact. At the top of the next screen is a field of how it's connected. Yours probably says 'Phone.' Change that to 'Google,' which also shows your email address.
I never did figure out how to change an existing contact connect via, ended up just doing them all over again with the Google connect. Wish I knew that trick but starting over correctly will work.