Lyric discussion by Duiel 

Cover art for Pug lyrics by Smashing Pumpkins, The

i think pug refers to a pug machine, since he is changing for this one girl who he loves who is sort of abusing him. Or it could be reffering to different types of "pugs." When he says

yours alone

inside where it's warm wrap myself in you outside where I'm torn fight myself in two

I think he means that when he's with her (inside, where's it's warm) everything is ok but when he's not, he's confuzed and not really sure what to do.