Is it appropriate to promote my article to a professor related to the article's field?
Quite the opposite, I think. In mathematics, in the days before the Internet, people did this by mail. The mailed reprints of their published papers to their peers.

It is important to consider the time of people you interact with, especially busy people. Giving your professor a copy of the paper will take only very little time. He or she can then choose to read it or not and it would be polite to accept also the case that he/she does not read it.

In this sense, asking about feedback would be a completely different ballpark already, because that would imply asking him/her to read it.