I'm not sure if you were going with your mom because you are a minor or just for support (both are great!), but:

If you're a minor, depending on your age in your state (or country if that isn't applicable), you may be able to speak with your doctor privately, and legally, if you tell them you don't want your parents knowing, they cannot tell them barring extreme circumstances. If at a certain point you feel you are ready to share your struggles with your mom, having the doc explain to her privately rather than you alone might be a more attractive option, since the doctor can provide facts and some practical perspectives and advice.

In this case, or if you are just going with your mother for moral support, perhaps if you tell your GP that you are struggling with an eating disorder, they can prescribe some advice and defer your mother's worries or, possibly, nosiness if that's a problem.

Also, it is important to be straight forward with your doctor, as you are paying for their help and if they don't have the facts and true figures, they can't provide accurate help or advice, so in the most petty sense you're not getting your money's worth either.