Is it appropriate to promote my article to a professor related to the article's field? Pardon but I couldn't find a better title for my question.

I am one of the editors of an undergraduate journal, created alongside 2  other undergrads of the same school, in which we publish upper-undergraduate articles related to our school courses(mostly expository, sharing our love about our studies). We publish the journal both online and in print, with printing costs covered by the faculty.

Is it appropriate if I publish an article related to, for instance, fluid mechanics, to pass the journal volume in which my article is featured to the professor teaching fluid mechanics in my school?? Will this be considered as a 'showing off'? I

would like to mention that the professor knows me well from the first year of my studies in which I expressed to him my interest in his field and asked for extra references for self-study.
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.