No, it does not work here. Put up is used when something is assembled or secured to a wall. Even if it were an art exhibition, although you might put up the pictures, you would put on the show (or exhibition).
"Put up" can be used to mean "engaged in" or "came up with". He put up a fight. He put up a great effort. So in your sentence, "show" could be understood as "effort", if you use "put up", which is still very similar to what your teacher wants to say.
If you're referring to the actual show, "put on" is better.