The only context in which I've heard outside in is the TV show Inside the Actors Studio, when students ask actors "Do you work from the inside out or the outside in?" In this context, inside out/outside in are opposites.
ETA: in the Siouxie lyrics, I think it's just a play on words, without much specific meaning.
Oh dear me.
Since I was a tiny pup, outside in was always understood to be a flippant whimsical term meaning exactly the same as inside out. If the inside of my sock is out, then the outside is in.
It's still a family joke. When WMPG complains that her socks are inside out, I try not to ask every time if she's sure, because I think they are outside in. There is a limit to the number of those "I've heard that before and I think you're daft" looks I can take in a week.
In this context, with from, it means from the outside to the inside.
Sometimes this is used to describe looking in through a window, or figuratively to describe someone who is an outsider trying to understand the culture of a group that interests him.
In this case, though, I think it means "every part of me, from the outside of me right through to the inside."
Your intrepid reporter reporting back from the front.
Google kept finding blog references to outside in; not very helpful to my cause.
So with sinking heart I turned to my old friend the OED.
Sink no more, my heart http://ww.mibrujula.com/foro/images/smiles/incon_24.gif 1681 in S. Pordage tr. T. Willis Remaining Med. Wks. Table, Inverse, a turning inside out, or outside in, upside down, quite contrary.
..... 1863C. KINGSLEYWater-babies i. 18 He did not know that a keeper is only a poacher turned outside in, and a poacher a keeper turned inside out.
We use 'outside in' to describe things like garden rooms or conservatories where it is as though the outside has been brought indoors. There is even a restaurant near where I live called The Outside Inn, which is decorated like an indoor street.