Cellular carriers often place lots of restriction for people who want to do exactly as you do. Once in a full moon maybe OK. There is no such thing as unlimited by the way, real world have limits, is matter how that's served to you.
Bluetooth is for audio only.
You could use Chromecast to do that if you have WIFI or if your phone supports MHL you could get an adapter and connect your phone to an HDMI input of the TV.
Cellular carriers often place lots of restriction for people who want to do exactly as you do. Once in a full moon maybe OK. There is no such thing as unlimited by the way, real world have limits, is matter how that's served to you.