Post History

A useful way to think about this is, every story you write is set in a world of your own invention, that sits in some relationship to the real world that we live in. The real world that we live in includes J. K. Rowling and the Harry Potter books. (Which created a world of their own that sits in some relationship to the real world we live in.) You can include the existence of those books in your invented world, just as Rowling can include the existence of Kings Cross station in hers. 

The world you create can be a world in which the Harry Potter books exist, just as it can be a world in which the Bible and the works of Shakespeare exist. Thus characters in your stories can make reference to characters in the Harry Potter books, just as they can make reference to characters in the Bible and in Shakespeare. Thus saying that your character looks like Harry Potter is fine, in principle. 

What is not fine is setting your story in the world that J. K. Rowling created for the Harry Potter books. That is not our world. That is her world. Setting a story in that world, or a world derived from that world, explicitly or implicitly, is wrong. (Unless it is done for purposes of parody. See _Bored of the Rings_, for example.)

There are some technical restriction on top of this. Just because you set your story in a world in which the Harry Potter books exist, does not mean you can quote large sections of them verbatim. But the general spirit of the think is that you can populate your world with the artefacts of this world (the Harry Potter books, qua books) but not with the artifacts of other writer's invented worlds (Hogwarts, or anything obviously derivative of Hogwarts, for instance).

This does not mean you cannot have a school for wizards, of course, or Ursula Le Guin (to pick but one example) would have had a massive copyright claim against Rowling. It is not the general features of an invented world that are off limits, but its specifics. We can all play in the same sandbox. You just can't take my sand. 

But this is all the principle of the thing, as regards but the law and the honor of the profession. Specific laws vary from one jurisdiction to another and if you feel you are in danger of violating them, consult a lawyer, not the Web.