I think Laurie has given you some excellent advice. The key is to document everything - dates, words, actions and witnesses (e.g. the nurse). Make your reporting as EMOTIONLESS as you can. Just the facts! For example, do not say "I don't approve of how she treated my son." Say "Mrs. X put her right hand on Joey and pushed him sideways into the back of the bench. Nurse Y witnessed this incident." Then factually say that "Joey wiped a tear from beneath his eye and Mrs. X moved to within 8 inches of his face and said...." Have your husband read it over, and also a trusted friend - make sure it is solidly proofread for errors in grammar or spelling as this will help your case. Sign it first, then make copies. This information goes to the principal as well as the superintendent of schools. Whether you give it to the teacher or not is your choice - the principal will certainly share it with her. You want to make sure that the principal and superintendent receive it FIRST.
Document what your child said about being told not to throw up.
I'm pretty sure it's illegal for teachers to forcibly touch a child that way. Guiding a child into line or onto a bus is one thing. Touching a child or restraining him to prevent physical danger is acceptable - for example, a kid taking a swing at another on the playground. But in a controlled situation like the nurse's office? Uh uh.
The only thing your child is lacking is experience in a school setting. The other children who have attended preschool already know some skills about lining up, sitting in a circle, listening to the teacher, etc. If your child is the only one with no experience and he's in a room of 18 or 20, it can be overwhelming. The other kids are doing things instinctively at this point but it's completely foreign to your child.
You also should be extremely open to the fact that 5 year olds don't always tell things exactly as they happened. They embellish, they misinterpret, their fear colors their explanations. You MUST allow for the possibility that a) your son was not in control at the school to start with, and 2) he might not have told you the story exactly right. This might not be an intentional lie - it might just be his perception in the middle of being extremely upset. However, all this throwing up is clearly indicative of a stressful situation - once a kid is throwing up, NO ONE should be telling him not do or saying "We don't throw up on the floor." But make sure that's exactly what was said - and it's not just his perception that throwing up is a bad thing and therefore the teacher must have been angry about it.
I would absolutely pursue this situation with the school administration. If you are not completely satisfied with the superintendent's response to you and whatever action steps she plans to take, you need to give your documentation to the police. They may not have enough to go on, but they will have it on file. Do not threaten to press charges against the teacher to her face, and do not threaten it as a way to get the administration to do something. Also, personnel matters are confidential so do not expect the superintendent to tell you if there have been previous complaints, or to tell you what has been said to the teacher. You CAN ask what the policies and procedures are in cases like this. Don't be intimidated if they say this has never happened before. They have to have procedures in place long before there is an incident.
I would also look at some short term therapy for your child so that he can process this incident and realize that not all teachers and not all school situations are the same. Otherwise, what happens the next time?? Start with your pediatrician and then see about a referral. Your pedi should be advised of this excessive vomiting anyway - maybe start with a phone call and see if the pedi wants you to come in.
You could consider putting him in a pre-k class that is smaller and in a different location entirely. He might do better in a class of, say, 12 kids than in a class of 22 (or whatever the size is of his current class). Going there by car with you and not dealing with a bus, but still starting in a classroom experience, might be beneficial. Home-schooling has been suggested, but frankly, this issue is not about academics - it's about socialization, being in a group, dealing with structure and authority, etc.