How do I make the Messages that are sent to me stop going to my Mac?
Open iMessage on your Mac and go into Preferences. Choose Accounts and make your changes there. That should fix the problem with the Mac. You should go to your phone, open Settings and make sure your iMessage is turned on. Your iMessage must have been turned off on your iPhone. I receive messages on my MacBook and phone but can easily turn one off by going to the settings.