In Bihar al-Anwar, vol. 20, p. 73, it is somewhat vaguely ascribed to 'Ikrimah that during the Battle of Uhud, the words of Nad-e-Ali were called down to the Prophet (S) from the heavens. 

(Specifically, this narration does not include the phrases bi-azamatika ya Allah or bi-nubuwwatika ya Muhammad)

To my knowledge, it does not have a chain of transmission and it is not specified in any of the classical Shi'i hadith books as a du'a.

Since Sufis also recite this du'a frequently, possibly Sufis first used it as a du'a, and then it became more common en masse among Shi'is. It is hard to say.

However, part of the merits of a du'a lie in its effectiveness. Since many people recite this du'a for a specific matter, and find that their prayers are answered quickly, experience shows it is a helpful and effective du'a, regardless of its origins. Seeking intercession from the Prophet (S) and Ahl al-Bayt (A) as a general act is acceptable.  

There is also no problem if one does not wish to read it because of theological reasons, absence of strong sourcing, or some other matter. 

Personally I read it sometimes.