Kira thanks for the link.
OP, I think it's hard for non-trans people to understand gender dysphoria as anything other than "anxiety" or "stress". There are a bunch of articles online describing what dysphoria feels like; maybe if you use one of those as a starting point to write your own experience on paper and give it to your parents, they might start understanding that this is more than your standard anxiety and that there is a solution that will bring about relief.