If you’re a native English speaker, there’s an easy trick for remembering whether you should say “look at this picture of my mom and me” or “look at this picture of my mom and I”: Remove the words “my mom and.” Because you wouldn’t say “look at this picture of I,” you also shouldn’t say “a picture of my mom and I.” You can apply this to just about any phrase with potentially confusing pronouns, and it’ll work the same way. For example, because “her went to the store” is incorrect, so is “her and I went to the store” — it’s “she and I went to the store.”
This trick for relying on what sounds right will work best for native speakers who grew up hearing people speak in correct and natural rhythms. To get a bit more technical, we need to distinguish between subjective and objective pronouns. The former refers to the subject of a sentence, while the latter tells us who is performing or receiving an action. I, you, he, she, it, we, you, and they are subjective pronouns, whereas me, you, her, him, it, us, you, and them are objective pronouns. The two types of pronouns are paired with different parts of speech and therefore have different meanings. An objective pronoun (“me”) would follow a preposition such as “with” or “between,” while a subjective pronoun (“I”) is paired with a verb.
To sum things up, if there’s a preposition such as “between” or “with,” the proper phrasing is “between you and me.” That’s because the preposition needs to be followed by an objective pronoun rather than a subjective pronoun. Test this by switching the pronouns. If you say “between we,” it’s clear that you’re using the wrong pronoun.