Your network provider knows your DNS lookups and your location. Even with a burner this may be enough information to identify you and track what you're doing.
If you're just worried that the NSA (or someone else) is storing all your messages then WhatsApp or Telegram would be fine. However if you're a person of interest then both WhatsApp and Telegram could give away your network. i.e. not what you say but who you chat with.