Well, you sort of do want medication in order to feel good-or at least better-which isn't a crime. I'm sure if they suffered from anxiety or depression they would want to "feel good" too.
The answer to your question isn't quite so easy, as people are very stubborn. Adults, especially. Depending upon what sort of people your parents are, you may never convince them of the legitimacy of your mental distress. Unfortunately misinformation over mental-illnesses is widespread and it can be difficult to explain to a person with a, for lack of a better term, healthy mind to comprehend that if you could simply change your thoughts, you wouldn't have anxiety or depression. Hell, all mental illness would be eradicated if such a ask were that easy! For the time being, your only option is to continue attempting to explain your issues, which can be quite aggravating when your parents simply won't listen. Regardless of what your parents think or whether they allow you to take medication (which they should. No parent denies their injured child pain medication because they feel the child wants them to "feel good", but I digress.) you should focus on feeling better, mentally. I'm not entirely sure how one goes about doing that, but this website seems a smart place to look.

Despite having nothing of real value to say, I responded to your post for the simple reason that I do not like questions to be left unanswered. Hopefully somewhere in the midst of my ramblings, you will find something helpful.