I am not an expert, just a mom with ADHD kids. You ought to get an official diagnosis, meds, and a 504 plan. You cannot do that without your parents’ help, so you will need the help of other adults who can bring them to seeing you differently. Here are my ideas: 1. If you have a pediatrician/doctor visit planned soon, tell your pediatrician. It might be difficult doing that with a parent present, but since you are 13, your doctor may ask them to leave the room so that he can talk to you alone. Take the opportunity to speak with her/him at that point. Bring the letter you wrote to speed matters. If you fear you will not have time alone, call ahead and ask the receptionist to leave a note for your doctor that you want to speak with him/her alone.
2. When school starts, try to get an appointment with the school psychologist. Talk to your counselor, to a favorite teacher, to a teacher who always fidget (I bet he’ll know what you are talking about). Ask them to quiz you on your favorite topics to show them that you are smarter than your grades would indicate, bring the letter you wrote today. Find an advocate. All of those avenues might be terrifying, esp. if you have other anxieties associated with your ADHD, but you need to speak up for yourself in order to get the help you need.
Btw, 13 seems way to0 early to be taking the SAT. When you try after you have had the courses you need to succeed, a year or two to mature, 504 accommodations, and adequate medication, you will do much better.