It sounds like she has a tactile sensory integration issue. It is not too uncommon although many children outgrow it. She sounds to be over sensitive to the feeling of restrictive clothing on her body. In other words, she can't "tune out" the sensation of the clothing restricting or rubbing against her skin, so she notices it all the time and it is distracting to her. The kind of specialist to consult- if you want to- is a Pediatric Occupational Therapist. If you discuss it with her doctor you may be able to get a referral for one through your health care. Meanwhile, think about which clothing she does like to wear- loose fitting? skirts? dresses? no elastic? etc.. and try to purchase for school what she is comfortable wearing. You might see if a certain "cut" of underwear feels better to her (hip hugger vs. bikini) and also try some that is too big, not too big to fall down but loose fitting. Different fabrics may be more comfortable than others for her, too.
I bet when she gets her periods she'll wear underwear! Even if it's against her will!
By the way, when I read this that she has always had clothing issues---- have you ever looked up sensory integration or processing disorder? This is a pretty classic sign of it. The thing to do is to find a type she likes (seemless, no tags usually is best of a material she prefers) and then buy tons of that same kind. I tried about 20 different kinds of socks, found a type my son likes and have a whole drawer full of that same sock. He doesn't like tags in clothes, seams that he can feel, or jeans. Is your child a super picky eater?
So, no matter reasoning or thought process . . . I think we have to have rules for our children. Undies are a must. I have a son with sensory integration disorder which is a neurological delay and tactile issues arise with clothing. This especially can include socks. He NEVER wants to wear socks especially at home. This started when he was little. We had to compromise. He can be sockless at OUR house but not at other's houses. He has to wear socks when he leaves the house as well. Rules and boundaries give him an idea of what is socially acceptable and yet, allowing some freedom at home. Perhaps you can go with allowing her no underwear in her own bedroom. But this is a parenting moment in which we make the rules. good luck