Answer:
The dog: freedom
The White Umbrella: American culture
Step-by-step explanation:
The dog represents freedom. The narrator feels a strong desire to return to his country, Dominican Republic, where he will find his dog and be able to have fun with him outdoors, where no one can judge them, because they are free. The dog brings that feeling of freedom and that is why he is so desired by the narrator.
The white umbrella represents the American culture that the narrator so desires to reach, but which seems increasingly oppressive and exploratory to her. When this umbrella is thrown into the sewer, it symbolizes the rejection of American values and their false moralisms.