Recently I allowed my laptop to get messages that have been sent to my phone, but that was a huge mistake. I have a macbook air and I do not need to disconnect my phone from my laptop, I just need to disable my laptop from receiving or even seeing my messages.
Open Preferences in the Messages app and log out of your Apple ID. That will prevent your device from receiving any messages there.
Additionally you can disable message forwarding in the Messages settings on your iPhone.