There's nothing wrong with inside there except that it would usually be accompanied by with you in that particular question.
Do you have your mobile phone inside with you?
There, inside refers to the interior of some place which is important in context.
A pedestrian taking a shortcut through an alley hears banging on the metal door of a restaurant kitchen:
--Let me out! The security door locked automatically and the kitchen is on fire.
There's no way for me to open it from the outside. Do you have your mobile phone inside with you?
-- Yes, I do.
Take some pictures for social media while I run and get help.
But in other statements it would be idiomatic for the word to stand alone:
I left my umbrella inside.
There, inside means "indoors", that is, inside the house or inside some other building which one has exited.
That was a pretty good restaurant! But it's gotten a lot colder while we were having lunch.
-- That reminds me, I left my coat inside!