I think it's TCU

https://en.wikipedia.org/wiki/TCU%E2%80%93Texas_Tech_football_rivalry

https://en.wikipedia.org/wiki/College_rivalry#Big_12_rivalries

https://en.wikipedia.org/wiki/List_of_NCAA_college_football_rivalry_games

https://en.wikipedia.org/wiki/TCU_Horned_Frogs_football

These are the reasons why I believe Texas Tech is TCU's biggest rival and vice verse please let me know what you think