I can’t send my messages through my own number but it’s rather the iCloud which isn’t always done as so

Go to Settings > Messages

and make sure that iMessage is turned on. You may need to wait a moment

for it to activate. Tap Send & Receive. If you see "Use your Apple

ID for iMessage", tap it and sign in with the same Apple ID that you use

on your Mac, iPad and iPod touch

See if anything here helps.

An older article, but see if the troubleshooting helps.

Handoff Continuity Troubleshooting.   -

iPhone, iPad, iPod touch, and Mac using Continuity - Connect.    *

How to forward text messages on your iPhone.   *

SMS Relay - Set up and use –Yosemite/ iOS 8.   -

SMS Relay - Set up and use –Yosemite/ iOS 8  (2).  -

Text messages forwarding.   -