First time sick? Why come to work ilI? Thowing up? Perhaps she should have called or visited her doctor for a excuses sick day off? Couple days?
Illegal, she'll have to check with HR on sick policy.
I knew a woman who was always sick, she could make herself cry, throw up and fall out at will. Last "sickness" episode employer told her she could go home and file for unemployment or use the trash can. She throw up all day. 2 days later they fired her.
That being said it depends on your company's sick policy.