Is this a 1961 proof Philadelphia? And in the picture with my fingers is at the "mirror like finish" that everybody's talking about?
Yes. The mirror like surface is a key indicator. Matte surfaces are also possible. Although you are handling your coin by the edges, it should be done with gloves. Otherwise you may impair your proof.
"Although you are handling your coin by the edges, it should be done with gloves..." This is one of those "Do as I say not as I do" things in the world. "Don't drive above the speed limit" is another." It is a choice. In my experience, gloves are used for photographs and in the Numismatic Collection of museums when someone who does not work there is present.