I'm not being funny, but your parents don't have to "let you" get medication that will improve your life.
You book an appointment with your GP, go, they don't need to be there. Take time out of college if it makes it easier to go - explain to your teacher you need to see your doctor and that you'll catch up with all work.
But your parents should never try and stop you from doing this when you're suffering. I can't even understand their thinking on this one.