So I know that it's correct to say:
Jane and I are going shopping
I shouldn't use me here because (as stated on Oxford Dictionaries Online) I is what I would use in the singular form of the sentence:
I am going shopping
But does this same rule apply if I want to (impolitely) put myself first in the sentence? Should I be saying:
I and Jane are going shopping
Because this just sounds incredibly wrong. It sounds much more accurate to use me here.