“Swe” is another way of saying “swoje”—so it’s a reflexive pronoun.
The form “swe” is considered archaic or literary. It is mostly used when talking about lofty or romantic things, often while employing metaphors. So you’ll often see things like “swe serce”, “swą miłość” or “swe życie”.
If you use the shorter reflexive form when talking more ordinary things (e.g. clothing items), it might sound a bit comical/ironic.
The short forms decline just like the long reflexive forms (“swój”, “swoja”, “swoje”). The only difference is that the oj / ój in the middle is taken away. You can look it up on Wiktionary: https://en.wiktionary.org/wiki/swój#Declension_2.