Texts show up on my computer but not on my iPhone

Some, not all, of texts that I send and/or receive, all show up on my Mac but not always on my iPhone. I checked my settings and message forwarding and all is set up correctly. I have iMessages and Text messages turned on.

What is going on and how can I fix it?

I'm a Realtor and rely on my phone when I am out in the field.

Please help!