Yes it is possible by using the techniques of Cryptography. What you are essentially asking for can be achieved through End-to-End Encryption & Decryption (E2E).
Encryption means converting from understandable format (normal) into non-understandable format (this is called cipher). Decryption means the reverse. So if you want any file (pic, video, audio, text) to be understood only by the receiver, then before leaving the network, the file should be encrypted at your end, this way even if the file goes through the network and servers, they cannot know how to decrypt it, because end-to-end encryption means only the two ends (i.e sender & receiver) only knows the secret key to unlock it.
Today, WhatsApp & Telegram both of them have implemented End-to-End encryption. Facebook messenger has no such encryption. So it is not safe to use facebook messenger to communicate sensitive information. But WhatsApp is not Free Software, therefore we cannot verify if their implementation is correct or wrong or if it have backdoors etc., essentially end-to-end encryption means there should not be any backdoor (i.e except the sender and receiver no one should be able to unlock any message for you).
This is like you and your friend sharing two keys of a same lock. Only until you both have the keys, it is safe for you both, if a third person also has the key for the same lock, then it is no more safe. Telegram’s desktop & smartphone clients alone are Free Software. The end-to-end encryption can be verified there, but Telegram’s server side is closed proprietary software and it is a centralized platform, therefore we can safely reject it. Also Telegram’s encryption algorithms are not battle tested, it is considered unsafe in crypto world.
That is the reason why we as a community itself started moving away from centralized and partial open platforms like Telegram and towards using Riot/Matrix combination. Riot has implemented end-to-end encryption and it is Free Software. Matrix is the underlying protocol which Riot makes use. Matrix protocol is a decentralized and federated. You can enable end-to-end encryption and share messages and files safely among your friends there.
Other options are,
Gnu Privacy Guard (GPG) in both computer & phones.
Simple rules to follow when choosing an app for communication,
- Check if it is Free Software or Open Source.
- Check if it has support for end-to-end encryption.