So I actually tried your code and it works for me. Exactly the code you shared without changing anything other than the name of the fields. Maybe you had a typo with your media name?
{
"data": {
"me": {
"id": "2",
"email": "pasd@asd.com",
"firstName": "asd",
"lastName": "wqe",
"picture": {
"data": {
"id": "2",
"attributes": {
"url": "/uploads/Harry_1_e3a9ddd11c.jpg"
}
}
}
}
}
}