How do I record my iPhone's screen and sound whilst recording my mic
You can use the built in screen recorder in your iPhone. If you’re using iOS 11, it will record the sound from whatever source or website, and you can also select mic, and get both audio recordings.

To record your iPhone's screen. Go to Settings app → Control Centre → Customise Controls, and make sure to add Screen Recording to the include list.



Now to record your iPhone's screen, swipe up from the bottom of your screen (swipe down from top right on iPhone X) to open Control Centre.



There is a circle with a solid dot in the middle, just press and hold it, it will open and ask you to record screen and if you want to record audio from the microphone as well.



Once finished, swipe to open Control Centre and tap the same recording button to stop. The recording will be saved to your camera roll.