Grammar Lesson

Now, I don't pretend that my grammar is perfect, but I do think that I have a better grasp on the workings of the English language than the average schmoo. In fact, one of my biggest pet peeves is bad grammar (I won't even get into how deeply annoyed I am by what the internet has done to the written word). Imagine my surprise when someone accused me of breaking a rule of grammar. I still maintain that I did no such thing, of course. Okay, generally one would say "Sally and I went to the park this afternoon," not "Sally and me went to the park this afternoon." This is because you would say "I went to the park," not "Me went to the park." It makes sense to me then, that if you would say "George showed me how to cook," you would also say "George showed Sally and me how to cook," right? I mean, you certainly wouldn't say "George showed I how to cook." Anyways, that's my problem, so I bring it to you. I know that many of you who read my blog are better writers than I (I've always been stronger with speaking than I am with writing), so tell me, does what I am saying make sense?