yes, a psychologist knows more about anxiety/depression etc. but oftentimes the family doctor needs to see you first and then they will refer you to the psychologist. When you tell the Dr. what you've told us, he/she will most likely take it very seriously. And you need to specifically tell the Dr. you believe it is all from anxiety and you are desperate for some relief.
Ditto the above, though I'd see a psychologist rather than a doctor. Your parents' biases are odd at this point in time, but it was very common when I was your age. Your parents need an education, but in the meantime you need help now. Good luck.
IMO, from my own experience, you need to get to a make an appointment to see your doctor ASAP. You can't allow your parents' beliefs on this to dictate your well being. Have a friend or someone else bring you there if you can't rely on your parents to take what you're going through seriously.