I finally solved this issue. Somewhere along the way either an update on my iPhone or iMac caused any iMessages being sent from my iMac to be from my email address instead of my phone number.
I went onto my iPhone and went to Settings > Messages.
My phone number was there and checked, but none of my Apple ID's/emails were listed. So I pressed the button at the top, it said something like "Use your Apple ID", and then it added my Apple ID's/emails as well.
I then restarted Messages on my iMac and it asked if I wanted to use my phone number. I then went into settings for Messages on my iMac and clicked the dropdown for "Start new conversations from:" and my phone number was now available.