Everyone including I

When you determine if you are to use “me” or “I” isn’t it the rule that you are supposed to ignore the words relating to other people? For example “John and me went swimming” is wrong because “me went swimming” isn’t how ya say it.

Here I am now really confused when it comes to sentences that have “everyone including”. To illustrate: “Everyone including me went to the show” is the way I’ve been saying it my whole life, but it just dawned on me how asinine it would be to say just “me went to the show.” However, “everyone including I went to the show” sounds equally asinine, but can this be right?

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