Good day to you Aoifeaok98,
It sounds like when attempting to connect your TV to your iPhone’s hotspot, the connection is not succeeding.
Can you tell us a bit more about what happens when you try to establish the connection? Is there an error message? If we’ve understood correctly, you mentioned that the TV also broadcasts its own hotspot, which your boyfriend’s phone connects with. Will your iPhone connect to the hotspot the TV broadcasts?
The following article also goes over some steps to take when having a issue with Personal Hotspot - If Personal Hotspot is not working on your iPhone or iPad (Wi-Fi + Cellular
Thanks.