I want to start runs but I don't know how I am going to record my runs as all I have is my switch, a tv screen and my phone. Would a recording of either the docked switch on tv screen or the undocked switch on the switch screen be acceptable as long as everything is clear?

Phone recordings are fine! Main things that are important are being able to see the full screen and having the milliseconds on the timer be somewhat legible. If you post an example video here we can probably confirm whether or not your setup is good for submissions.