I can't send messages to anyone in my contacts except to myself
Use the Messages app to send and receive messages.

Send a message

Open Messages.
Tap the Compose button  to start a new message. Or go to an existing conversation.
Type your message.
Tap the Send button .



Use Messages on your iPhone, iPad or iPod touch

Pressing Compose lets you type a phone number or email address to send a message to.
The list of email addresses and phone numbers in your screenshot of Settings are what other people type in their compose box to send you messages. You don't add other people's contact information there.
If you get an error message when trying to send a message, Apple has debugging steps:

If you can't send or receive messages on your iPhone, iPad or iPod touch