Someone sends you a picture of themself with another person. They title
it Me and John. Should it be John and I?

Ah, it's a good question. The answer is both are right. It's because it depends what words you understand to be missing.

Here is a picture of "me and John".

"John and I" stood by the sea.

There's more on me and I here.

There's a related lesson on me and myself here.