Does my child have ASPERGERS or have AUTISM?!?

She's extremely smart. But has social problems. She doesn't like to approach people to ask questions. Even when forced. Or walk up to new people. Just hangs around people she knows. She also has a problem with clothing. Usallty wears the same outfit for 2 weeks. Yes 2 weeks. Also we have huge fights about clothes and shopping. Always worried about others opions and acceptance. Shes a 4.0 student in math and science. Yet hates school and homework. She loves and spends all her time on research online on astro physics and space chemistry on her own. Yet can't spell well or write a paragraph on her own. She takes college credits for physics and in AP programs and reads books about phyics and space. Yet has a breakdown(crying and fighting) if she has an english report. Shes 15. Does she have AUTISM?