It should be "me and her", because those are the pronouns you use when you are referring to the object(s) of a sentence. If you can't decide which to use, try using just one pronoun at a time. E.g.
Why did everybody do something but she?" isn't right, and neither is Why did everybody do something but I?"
But Why did everybody do something but her?" is right, and so is Why did everybody do something but me?"
So the correct sentence would be "Why did everybody do something but me and her?"
To answer your other question, I'm not sure of the rules regarding "only" and "just", but I think they're often interchangeable. I could only tell you which to use when given context.