To be honest, and this might sound mad, I enjoyed my GCSEs. I was confident, I found sitting in the sports hall listening to the whir of the air con very relaxing, I had a pen that wrote beautifully, and I was sure I could do as well as I needed to. I was right.
A Levels on the other hand were another matter entirely. I found them much more difficult than my GCSEs and as such found the exams and the approach to them much more stressful.
What I would say though is that your exams shouldn't be stressing you out to the point that you can't even bring yourself to sit down and revise. Certainly not at GCSE level, with almost a year to go until your exams start.
I think what your parents say is right, for GCSEs at least. If you put in the work, you will reap the rewards. Make sure you attend any revision classes that your school provide you with, and start revising now.
If you find that you are so anxious that you can't even think about studying, you should see your GP because you may have an anxiety disorder - nobody should get that stressed over exams.
Have a chat to your teachers and see what they suggest. Also, if you have friends doing the same subjects as you, set up study groups to discuss the course content. My friends and I used to play "Jeremy Kyle" and set up scenarios related to our courses which meant we had to debate issues etc. It might sound stupid but it was a laugh and it really, really did work.