C.A.
Though I am a stay at home mother now, I taught first grade for 12 years. Yes, I have seen this before. The first few days of school when I get a child like yours, as a teacher, I try to get to spend a few extra minutes with her when she enters the classroom. I find that if I make the child feel special it offsets her fears. Sometimes I have given them a special stuff animal to hold for awhile.
This behavior is really normal for her age. It takes 6 to 8 weeks to 'get use to' first grade. She will be exhausted. Often, kids fall asleep after lunch right on their desks.
At home, I would read books about going to school. Point out all the good things that happen to the characters while they are at school. Make sure she is going to bed extra early to offset her exhaustion.
If she continues to thow up and have stomach issues, I would make a chart and for everyday she can get to school and stay, she can color in a square. At the end of ten squares, perhaps you can take her for an ice cream cone or buy a small gift to celebrate.
If she does not stop thowing up I would then go see a doctor. It's not good to throw up so many days in a row.
She will be fine in the end, take it gentle with her because this is a big step in her life and school is very academic these days.
Good luck!