No, 'here you are' means you've been looking for the other people in the room, and you've now found them, so you announce this with 'here you are(!)'.
'Here I am' means you are announcing to other people that you have arrived, you would do this if they were expecting you and you think they might have been wondering where you were.
Hi dolcedell, it's ok, because "There you are." and "Here you are" in the context of walking into a room and saying it to people mean exactly the same thing. The only thing that is different is a tiny tiny detail that means you are mentioning "here/there" with reference to yourself, like close / far away but the difference really doesn't matter, as you're standing there with them.