Encrypted messages hide their contents from everyone but the recipient. They do not hide that you sent one. The two addresses, the time and the rough size are an event on a public chain, permanent and readable by anyone. There is also no forward secrecy: a key that leaks in ten years opens every message it ever received, because they are all still on chain.

Encrypted is the honest word for this. Private is not. Do not put anything here that would hurt you if the key were compromised later.