Can I make text messages disappear for both me and the other person?

While you can't delete messages for both parties, some messaging apps let you "unsend" messages, but only if you act quickly after sending them. Just keep in mind this might not work for all the messages you want to erase.

Unfortunately, you can't delete text messages from someone else's phone. If you delete them on your device, it only removes them from your device—not theirs. So those awkward messages will still be seen on their end.

If the messages are really bothering you, one option is to change your phone number. That way, any new messages would go to a fresh chat without the old history.