How long will it take to recieve my citizenship paperwork once my N-600 form is paid for and submitted?

up to 6 months

No, you don't.

The N-600 is for people who have NO other way to prove that they are US citizens. Think of a girl whose mom was knocked up by a G.I. during the Vietnam War in Vietnam after which the good soldier took off, only to be found again 25 years later in a dump in Kentucky. In such a case the girl has no choice but filing an N-600 that will lead to double DNA testing, proving that the sperm donor is her biological dad, and eventually a Certificate of Citizenship.

Since you became a US citizen by act of law, the Child Citizenship Act of 2000, your status as a US citizen is not in question. All you have to do is go to the nearest passport office with one of your parents and apply for a passport book and a passport card, so that you have two independent proofs of US citizenship. A US passport is the best proof of US citizenship there is, whereas very few Americans have a Certificate of Citizenship. Don't waste $600 on a piece of paper that is not good for anything but getting you your first US passport when you can easily get this passport without the piece of paper.

If both of your parents became citizens when you were a minor, you too would have become a citizen. Research this issue so that you do not have to pay for naturalization.