Sounds an awful lot like my D at that age (she is 16 now). Loonnggg tantrums, and many rules that we had to follow exactly (made me feel like a trained seal). She had trouble with personal boundaries -- she would get into people's personal space and make them uncomfortable without realizing it, which sounds like your D.
Ultimately she was diagnosed with a non-verbal learning disorder. ADHD tests have been "inconclusive". We have been told by testers that she would probably test as having Asperger's, while others assure us she wouldn't; we say she "flirts with Aspergers" because she is on the border. But we have no formal diagnosis.
She is also very bright, and has done well at programs like Davidson's THINK. She is super disorganized (that non-verbal learning disorder seems to be the culprit), which keeps her from knocking the socks off every class in school. But she does pretty well, especially with some organizational support. She has come a long ways socially. Still awkward sometimes. Still...she went to a robotics training course today, and told me at the end with a laugh that she had the best social skills in the room -- meaning that the others were REALLY poor at social interaction. But in comparison, she felt pretty good.
Hang in there, you are at the age that was hardest for us. It does get better!
