Your child's behavior is consistent with a child that has suffer a trauma. This trauma could be something she saw, something she heard, or something that was done to her.
One way to talk to your daughter is to ask her only yes or no questions so that she doesn't have to talk at all, she can just nod her head yes, and shake her head no.
One example of a question that you could ask, after explaining that all you want her to do is nod yes or shake her head no, is to ask if something bad happened to her.
If she nods yes, then you can ask another yes or no question.
It's a delicate thing to ask these questions, so keep them simple, and at her age level, and if she expresses in words or actions that she doesn't want to answer, you should stop, and try again later, or the next day. What you don't want to do is push her, because that will cause her more trauma, so take it slow.
Unfortunately, in my experience, a child that exhibits the kind of physical reaction you are describing has had something done to them, a person has hurt them, and if that's true then it's very possible that the person who hurt them has also threatened them with terrible things if they tell anyone. Typically the threat is that if the child tells, the person who hurt them will hurt their parents and/or siblings.
If something has happened to your daughter, she'll want to tell you, but she doesn't have the words, so gently asking yes or no questions will over a number of days give her a way to tell you.
Of course during the entire process it's important to reassure her that she is safe, that you are safe, and that you are listening to her, and you want to help.
Additional instructions on how to evaluate the answers that you might get from a child.
the questions: "did you hear something that bothered you," or "did you see something that bothered you," or "did something bad happen to you?"
the child shakes their head "no"
ask again the next day
the questions: "did you hear something that bothered you," or "did you see something that bothered you," or "did something bad happen to you?"
the child nods "yes"
ask another yes or no question, for example, "did this happen at home," or "did this happen at school," or "did this happen at the park," or any other location where the child visits regularly or has visited recently
the questions: "did you hear something that bothered you," or "did you see something that bothered you," or "did something bad happen to you?"
the child responds with an explanation
a) if the explanation makes sense, and the child greatly reduces or stops the unusual behavior, then the reason for the child's behavior has been found, and the reason for their behavior can be addressed, and the behavior is no longer an issue
b) if the explanation does not make sense, or the child does not stop the unusual behavior, then the process of asking yes or no questions needs to continue until the reason for the unusual behavior is understood, so the reason for the child's behavior can be addressed. When the reason for the child's unusual behavior is addressed, the behavior will lessen dramatically, or disappear completely.
Children use behavior to tell adults that something is wrong, or something bad happened, yet some children are so afraid and unable to find the words to talk about what's going on that they will tell stories to adults to try and get the adults to leave them alone, because that feels safer.
- if none of this works, it's time to visit a child specialist (a Pediatrician or a PhD. Child Psychologist) who can help the child talk about what is bothering them and what happened to them.
Sometimes a child can tell a trusted stranger what they cannot say to a parent or adult that cares for them. For the child, seeing a child specialist works best when the adults that care for the child and specialist work as a team to reassure the child and help the child feel safe.
While it's uncomfortable to consider the possibility that something bad has happened to your daughter, she needs you to be brave, to help her through whatever is driving her to be so afraid that she becomes physically ill.