Why are iMessages appearing on my iPad but not coming through on my phone?
I had the same problem.  Looking at Settings > Messages > Send &amp; Receive on both iPad and iPhone, my telephone number was listed under 'You can be reached by iMessage at' on both and was greyed out on the iPhone, but ticked on the iPad.

The fix was to:

(a) tap the telephone number on the Settings page of the iPad (Settings > Messages > Send &amp; Receive > You can be reached by iMessage).  This removed the tick beside the number, and

(b) on the iPhone, disabled and re-enabled iMessage (Settings > Messages), and then enabled the telephone number (Settings > Messages > Send &amp; Receive, and tapped the telephone number on You can be reached by iMessage at settings page.

A notification was then shown on the iPad: 


  Your Apple ID and phone number are now being used for iMessage on a
  new iPhone.