Personally I wouldn't tell your doctor you're fasting. Just ask for a general check-up, the kind they would do for some new jobs or to make sure you're not going to have a heart attack doing weights at the gym. They will just do the simple checkup for you just give them a good reason for having the check up so they don't start asking suspicious questions. I doubt they will though, they will be happy to do their 5 minutes work for your $50 or whatever they charge where you are.

Then you can let your parents know the doctor gave you a clean bill of health. I don't know for sure but I would be worried myself that a doctor would freak out about it. I myself send my kids to an alternative doctor on the rare occasions they need it, but even him I wouldn't trust with the knowledge I am fasting. I would be very worried that even he wouldn't understand and would try to intervene. I doubt it but after 20 days of fasting for example I wouldn't want to risk it.

That's what I'd do if I had to anyway. Good luck!

Andrew.