when you say something belongs to you, you don't call it "I's thing" - you call it "my thing".

if it belongs to your friends Jim and Bob, it's "Jim and Bob's thing" or "Jim's and Bob's thing". likewise, when it belongs to your gf and yourself, it makes more sense to say "my gf and my" or "my gf's and my", rather than inventing a brand new word that sounds so very stupid.