I'm so sorry this is happening to you. I agree with others who suggested to work with a therapist or tell your family that the issue is closed, but I realize these are hard things to do and not always an option.
Are your family members overweight? Sometimes people say these sorts of things out of jealousy or based on their own experiences. It doesn't make it okay, but at least you can know it's their BS and not about you.
I personally eat sweets from time to time - I was told I didn't have to be 100% perfect, just keep my eating choices good 80-90% of the time. But that may not work for everyone. I do agree that celebrating with food probably isn't the best idea, but a treat on your birthday sounds pretty harmless as long as you can enjoy a reasonable portion and it doesn't become a binge.
Good luck!