[OMFG!You'reActuallySmart!]

I'm not sure where you live but you're 19, presumably an adult so you may be able to make the appointment by yourself without the assistance of your mother, so that part seems like it's solved pretty easily. If you feel uncomfortable calling at home, then get the doctor's number (i.e. online), then use your cell phone or even a pay-phone.

Instead of nagging your mother over and over because clearly she has her reasons, why not ask her what her reasons are without nagging her? Some parents want to hope that their children will never get ill and may even go as far so as to do this, which although it hurts you, it can help preserve her belief. Or, it may be an issue she has with doctors, medications, etc... . Since you say you were officially diagnosed, I'm a bit uncertain as to the problem your mother has because some way or another, you got diagnosed and you say she's well aware of the diagnosis. So I'm unsure if she has an issue with the medications in general, and if that's the case, once again, you're 19 years old, hopefully you have some money saved up to buy the medications (assuming you already have a prescription).