Depresme - at first blush i was both confused and in agreement with you for myself that this was something i also am working on. BUt still being confused I went and looked it up:

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ni·hil·ism Audio Help /ˈnaɪəˌlɪzəm, ˈni-/ Pronunciation Key - Show Spelled Pronunciation[nahy-uh-liz-uhm, nee-] Pronunciation Key - Show IPA Pronunciation
–noun 1. total rejection of established laws and institutions.
2. anarchy, terrorism, or other revolutionary activity.
3. total and absolute destructiveness, esp. toward the world at large and including oneself: the power-mad nihilism that marked Hitler's last years.
4. Philosophy. a. an extreme form of skepticism: the denial of all real existence or the possibility of an objective basis for truth.
b. nothingness or nonexistence.

5. (sometimes initial capital letter) the principles of a Russian revolutionary group, active in the latter half of the 19th century, holding that existing social and political institutions must be destroyed in order to clear the way for a new state of society and employing extreme measures, including terrorism and assassination.
6. annihilation of the self, or the individual consciousness, esp. as an aspect of mystical experience.

Looking at that, do you think it is the right word for you? It seems so very strong. For me, my therapist is using the term "vagueness" because i have no purpose, no vision, goals, no caring about anything - kind of let the tide push me wherever.

SO, it is still important for me to figure out what is meaningful to me. and yet, it couldn't be a more difficult assignment since what i think changes with each hour, each day. For example, right now i am really irritable and argumentative and looking for fights. I really need to be writing a grad paper, but I could care less. It's due in 6 hours.
RIght now i don't care much about my family. I "hate" them all. TOmorrow that will change. I care about justice, my friends, my cat.... that may be all right now.
usually i care about art, music, school. doing well in therapy. i need to be caring about myself and stop harming myself.

i should stop while i'm ahead....