Sorry to hear your dd is ill. Similar story here (13 yr old started menstruating in the past six months). Was generally very active, energetic and sporty (did ballet seriously until last year). In fact, she was hard to keep up with.
Since that time she has been pale and listless, constantly tired, having lots of minor illnesses generally of the flu-ish-viral-glands type.
We've been at the doctors a lot, who have done about four sets of bloods over the past year or so. One set showed that she had been suffering from mononucleosis type illness that wasn't mononucleosis but similar. And that she is low in vit D. She isn't low in iron though.
She's seemed a bit better since then but is now pale and tired again (although she is under a lot of stress at school for various unavoidable reasons unfortunately). She is seeing ed psych for anxiety and exam stress (which can be very draining).
So, we've been placing a lot of emphasis on sleep (we make sure she goes to bed early and all technology is banned from the bedroom) but I have a suspicion that she is writing in journals/faffing around/doodling etc after lights out but short of telling her not to do it, or pacing about outside her door, or putting a camera in her room, I am at a loss as to what to do about that!
We are also making sure she doesn't eat too much rubbish (she would eat a lot of sweet things given the chance) to avoid sugar highs and lows and of course she is taking daily vit D and getting lots of gentle exercise such as dog-walking and gardening etc outside of school sports. And that she has a good balance of activities and relaxation ie friends - outside of school.
It's a difficult time when they are growing so much and I think I read that this period from puberty to adulthood is when the brain changes the most it ever will do in a lifetime. There are two or three dc in dd's class who regularly go home because of period problems and a boy who faints often. My mother used to call it "outgrowing your own strength!"
That probably isn't much help because your dd hasn't had gland issues or temps. But I just wanted to post because I think hormones can have a huge impact on a child. My dd was like a whirling dervish before puberty, and she is now completely transformed, much more hesitant, quieter, less active, in a dream half the time. It's a worrying time. 
I hope the latest blood tests give you and your doctor some more clues as to what is wrong, and I hope she feels better soon.