Showing off is essentially showing off one's pride. When you focus on yourself it's harder to see others for what they are, partially because you "project". projecting is a normal function in your brain that tries to associate everything with what you're focusing on, it's good for figuring out puzzles and concentrating on an activity, but it can backfire when you're too focused on your personal achievement when everyone thinks that you're showing off out of narcissism.
However, whether it's right or wrong you have to answer it for yourself. Our basis of morality is on the consequences of our actions. For example, I believe that there is one God, and that I will give account to Him after I die, therefore I follow His code of morality. I can say, with certainty, that showing off is wrong, and it's based on what I believe.
So there is one mental reason to not show off, you can look that up in many basic psychology text books. The moral reason is something that you need to decide for yourself.
In other words: Morality is just a way of saying that "I believe there are powers that hold me accountable for my actions." So instead of asking "is this wrong?" you should ask "Who is defining what is and is not wrong in my life?".
