According to my understanding, if you were NOT more than 18 years old on 27 th Feb., 2001, you are already USC when you became LPR and entered US as an LPR ( provided your father was a USC on that day of your entry into US as LPR ). One must enter US as LPR before 18 years age. You become USC by action of law and it is automatic. You only apply for Naturalization Certifiacate by filing N 600. You can file this N 600 during any time in your life as you are already a USC by action of law.
In that case you need to file N-600 for yourself . Both you and your father should be living permenantly in US as and when you apply and N 600 gets processed.
Alternatively, ( as Rahul suggests) you can file N 400 application as an LPR if you have cmpleted 5 yrs continous residency and meeting physical presence reqmt.