It’s a rule in English that “and I” is only used when it’s the subject not the object of a sentence. (Subject is the thing doing the action, and the object is the thing being acted upon)
The proper way to say this would be “she’s coming over me and my girlfriend’s movie night” because “she” is the subject in this sentence since she is the one “coming over”.
Hope that makes sense.
I pray to the universe that that last scenario won’t happen, but I’m totally doing it now if it does.