Yes, you have an eating disorder. It doesn’t matter what you call it. You are obsessed with your weight and what you are and are not eating and you are treating yourself horribly. Starving yourself (even for a day), giving yourself the dry heaves, and misusing your medications is not the way to get in control. Eating sensibly and doing a reasonable exercise routine is. You might also be pleasantly surprised by how things change if you take the diagnosis of celiac disease seriously. Going on a gluten-free diet is challenging but many people who have celiac feel much, much better when they drop wheat from their diet. See a nutritionist if you need some hints for how to go about it. You just might be able to substitute a healthy management of a gluten-free diet for your unhealthy approach to eating.
If you want to be in the art and fashion world, focus on making art and designs. Professionals in the industry are far more interested in the quality of your work than the size you wear.
Please show your counselor your letter. She can’t help you unless she knows the honest truth about what you are up to. Please don’t worry about “disappointing” her. Professionals do know that progress is often a matter of two steps forward and one step back. It’s part of the process. And by all means, let your mother help you. Your overconcern with your weight is threatening your health and your future.
I wish you well.