Is this an old painting that is in the public domain? If so, there is no problem copying it, especially as a teaching exercise. However, even some historical paintings are copyrighted by museums and collectors.
If she led you to believe the piece you are copying is her own original art--or if some of her paintings are copies of others' original works--that is disturbing, especially for a teacher. If it is still under copyright, I would begin by asking if she has the original artist's (or copyright owner's) permission to use the painting in this manner. If the answer is "no," I would tell her that this is a violation of copyright for which she possibly could be sued if the copyright holder became aware that she is profiting from this usage. (To say nothing of the bad example she is setting for her students.)
As far as what you do with your own painting, if it is a copy of a historical painting, I would make that clear however you may use it. (So as not to look stupid to anyone who may recognize it or like you're attempting to become a forger. ) While copyright registration and proof of someone profiting from infringement usually are necessary for an artist or copyright holder to seek damages, artists automatically own the copyright to their work from the moment of its creation. So if your painting is obviously a copy of another artist's copyrighted work, that would go in the closet.