They'll see how beautiful I am And be ashamed – (lines 16-17)
"Be ashamed of what?" you might ask. The obvious answer is, of course, "be ashamed that they ever enslaved African Americans in the first place." By asserting his race's right to all of the normal considerations that free people have in America, he is defining freedom as a kind of moral default position – all people are free and all people are beautiful, and to treat them otherwise is shameful.
I, too, am America. (line 18)
A lot of people associate the word "America" with the word "freedom." America is the "land of the free and the home of the brave," right? So when the speaker says that he, too, is America, he's basically stating that he, too, deserves freedom.