A determination can only be made after examining all the relevant documents and researching the applicable law.
You should retain an experienced immigration lawyer to review all the facts, advise you, and handle the case. You can find one through http://www.ailalawyer.com.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.
Sounds to me like you have a claim to citizenship but you'll need to have an attorney either file the N-600 or a passport application for you after collecting all of the relevant documents.
My answering this question does not form an attorney-client relationship. Always retain a qualified attorney before taking any action. My office offers free consultations.
Witihout reviewing all of the relevant facts and documents regarding your case I cannot provide you with a legal opinion on your citizenship status. However, based on what you have written, you are likely not a citizen as your adoptive parents did not affirmatively apply for your citizenship. I would be glad to discuss this further with you.
The above is not legal advice and should not be relied upon as legal advice.