If you are concerned about the ethics, it's strongly dependant on how you define your personal rules and how you apply them to the situation. One strategy to approach this with is to try to draw a line on what you will and will not do to keep it private. For example, you might decide: "I don't feel like I need to announce this to my parents or anything, but I will not to lie about it, should it come up". Where you draw that line is up to you, but it could help you approach your personal obligations rationally.
Personally, I would treat it like its not a big deal; the less effort it seems you put into hiding it, the less concerned your parents will probably be if they do find out.
Whatever you decide, good luck