Messages that I send from one device show up as new messages on other devices (iCloud)?

When I send a text or iMessage on one of my iCloud devices (my iPhone 7, or my MBP), that message shows up as a new message on the other device. (What I mean by "new message" on the other device is that the conversation has the blue "unread" icon next to it.) It's also worth noting that if my phone is locked, a notification will pop up showing that I have a new message from the person in the conversation to whom I sent the message from my MBP, even though the message a) is not "new" AND b) is not even from the other person- it's from myself. How do I fix this? TIA.

Wow, like, massive. How can this happen in 2018? The whole world is going to sh%t