I'm wondering how much tv she watches? And where (her bedroom, the family room, or somewhere else)? I'm assuming she's in high school, and you say she has a lot of school work, so when is she watching tv?
You could consider making a rule about limiting tv time. And you could make a rule about not eating or drinking in the family room or living room or bedroom. Eating is for the dining room table or kitchen table only. Not only does that limit mindless snacking, it keeps surfaces and floors cleaner.
And even if you're not driving her to an eating disorder, it sounds as though the topic of food and hunger is a common one in the home. And it sounds as though she's curious about why she's snacking, and restless, and hunger, to the point where she's upset.
So possible, one answer could be: helping her to evaluate her cravings (food, picking at nails, watching too much tv, etc). You might have her see a counselor to help get some strategies to replace craving behavior with helpful behavior. That does NOT mean she's mentally ill or has a diagnosis, it can simply mean that she needs some assistance in learning to manage some habits. You say she can't play a sport, but is she immobile to the point where she can't take a walk or ride a bike or do some yoga? If she isn't, perhaps consider enrolling her in a simple yoga class, or taking a walk with her. Don't talk about food during the walk, talk about guitars, trees, teachers, movies, etc.
Because it sounds to me like this is not about weight. This seems to be about a girl who isn't really carefully thinking about what her body and mind need, but instead is simply throwing food and mindless tv at her body and mind in order to get them to be quiet. A therapist can help her learn to listen to herself, to pay attention to what she actually needs (a brisk walk instead of watching another rerun of Friends on tv, playing the guitar instead of eating popcorn to keep her hands busy, for example). If you can't get a therapist for a couple of visits, then try encouraging her to ask herself "do I need to sit and watch tv and eat popcorn, or could I do something more useful?".