Which is Correct: I or Me?

If you are writing/speaking a complete sentence, you should use "It's a picture of Mom and me." The correct pronoun is "me" because it is the object of the preposition "of." You can simplify the sentence to read "It's a picture of me" which may help you choose the correct pronoun.

However, if you are trying to choose between "Mom and I" and "Mom and me" for the caption of a picture, and you are not using a complete sentence, you can use either one. They are both fine.

I hope this helps.