Ah, good question. To write an analytical paper on symbols in this story, you'd look at several things:
the meaning and emotional impact of the story
the role symbols play in creating these two factors
where you get the meaning of the symbols
As far as the meaning of the symbols, you'll want to start with explaining how you know that something is symbolic, rather than literal. A good example would be the wristwatch between the ribs mentioned. Is that literal? (Could that be a disease?) No. Then you'd look for symbolic meaning. Why might time be important in this story? To this writer? To this character? To the larger culture?
Answering those questions will get your essay going.