How would I record my screen on a Nintendo switch? If it is not free, may I use a phone camera or something to do so?

Phone recordings are permitted, so there shouldn't be any issue with that, so long as the entire screen is visible and not too many frames are dropped. If you want to get direct capture in the future, i recommend the Genki Shadowcast. it's only 40 bucks US and it works pretty well, according to people i know who've bought it. It mirrors your game screen into a window on your computer, so it's pretty good.

Thanks :D