I remember reading up that John thought Hey Jude was about him, and he said that the, "Go out and get her part" was about Paul's subconscious telling him to go get Yoko.
I think John may be partially right.
I do believe that Paul wrote the song because he worried about Julian and wanted to tell him that everything will be OK, but I think when he said, "Remember to let her under your skin, then you begin to make it better," was meant to say, "Listen, the only way it's gonna work is if you accept Yoko into your life as well, and then everything will be alright."
Any thoughts? I can't think of a single other thing the "her" can be.