Do you have a Samsung TV. I also think you need wifi.
I don't use a Samsung. I also don't have home wifi, but 160gb data with full tethering.
In my case I can run a Chromecast 2 on a now old Panasonic Plasma TV that does not have wifi on board; or when I'm staying at a hotel chain (Samsung TV's but irrelevant).
I can run the Chromecast off my Hotspot data MOST of the time now, although having a second phone as I do also tethered to the main phone does make it easier and works every time.
I still need the almost unlimited tethering, where you currently have only 10gb available. I think you would need a Samsung S series phone and a HDMI - USB C cable, or get a Hotspot allowance increase. I'm in the UK and most allow you to use the full allowance. If you're not stuck on a long plan you can't change, you could be SOL as said; but I could be wrong.