You want to add "own" from the English equivalent but there is no need for it.
It's an interesting question for translation (and since I do some translation of academic texts I'm always more interested in equivalence rather than literalness...).
English has no equivalent of the common Polish practice of omitting possessives when the context is clear enough... it's very hard to translate a simple phrases like
"A co na to mąż?"
"Z bratem rozmawialiśmy"
because in English you really have to have possessives (we'll leave aside occaional use of 'the' instead of a possessive "I spoke with the brother" which is highly... restricted).
So when a possessives do occur in Polish they seem more... salient....
how would you distinguish
and pilnuj sw(oj)ego nosa ?