It's possible!

For the "public" concern - Hubby just figured out how to send memos privately. If you login with memo key create your message with the hash sign first (#) then space and the message, submit and login with active key, then the memo is encrypted and only the recipient can see it if he/she logs in with memo key as well, respond and login with active key.

Here's the post https://steemit.com/steemschool/@iamstan/how-to-send-encrypted-messages-in-the-wallet

As for the app itself...are you talking mobile app or just web app?