As I was born in the U.S. I don't think I will need to proof that I am a U..S. Citizen.
Yes in that case you will not need any other documentation.
I am glad to hear. Do you know of other ways to apply for retirement benefits? maybe I should apply in person or can I call?
Yes, you can apply by phone.  Call 1 - 800 - 772 - 1213 or TTY 1 - 800 - 325 - 0778 from 7 AM to 7 PM Monday through Friday .