How do I unlink my iPhone messages from my iMac iMessages? I don't want my phone texts to show up on my home computer anymore.

The following from Connect your iPhone, iPad, iPod touch, and Mac using Continuity - Apple Support has how to turn it on. I suspect that you can turn it off by undoing the items 1 and 2:

To use Continuity for SMS and MMS with your iPhone and your Mac, iPad or iPod touch

• Your iPhone, iPad, and iPod touch need to use iOS 8.1, and your Mac needs to use OS X Yosemite.
• Sign in to iMessage on your iPhone, your other iOS devices, and your Mac using the same Apple ID.
• On your iPhone:
  1. Go to Settings > Messages > Send & Receive > You Can Be Reached By, and add a check to both your phone number and email address.
  2. Go to Messages > Text Message Forwarding, and enable the device(s) you would like to forward messages to.
• Your Mac, iPad, or iPod touch will display a code. Enter this code on your iPhone to verify the SMS feature.

Sign out in Messages prefs and use a different email address.