Streaming to the internet from an hdmi out port

I have a hirise camera (camcorder on a 25ft pole) that has a monitor so you can see what you are recording. I use it to film sports. There is an hdmi out port on the monitor. I am looking for a way to be able to stream the games to the internet via ustream, Facebook live, or some sort of streaming location that families can view the game that can't get to it. I have my iPhone and also a hotspot, and could tether a laptop to either of them. Is there any way to make this happen?
 
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