Not knowing the age of your child it is difficult to provide specific answers. However, two thoughts come to mind. First, a child may seem as if she is panicking and might hurt herself by screaming, but she won't. Young children often try this as a strategy to get their parents' attention and to control the situation. Secondly, as a parent and a teacher, I do not tolerate a child who hits, kicks, spits, etc. at others. When an adult makes body contact of this type with another, the person offended can press legal charges against the person doing the action. Therefore, I do not let children practice activities that can get them in trouble with the law when they are older.  

Think through your rules, expectations, and consequences. Are these fair and reasonable? If so, be ready to take action. Sit down with your daughter and talk about her unreasonable behavior. Let her know that her behaviors in these recent incidents were offensive to others, and people who handle problems in these ways tend not to have many real friends. Discuss with her how to behave appropriately. Help her identify situations where she might need help addressing a problem and how she should go about appropriately asking for help. Depending on her age, consider writing down steps she could use to handle problems on her own without hurting others. Role play various situations with her. Allow your daughter to be "Mom" while you portray the one with the problem. This simple technique will give your daughter a chance to practice appropriate behavior.

Next time your daughter begins to scream and fuss, give her a time out for a few minutes. (Consider assigning 2 min. for each year of age but no more than 10 for children six and under.) Unfortunately, as a good parent, that may mean that you take your child by the hand, take her to the chair, and wait with her while she sits. Set a timer, so your child will "see" how long she is to wait before she can get up. Don't look distressed if she screams or spits. Just calmly let her know you will start her time when she quiets. Once she sees that you aren't going to react, it will get easier. But, it may take several times of doing this before she understands that you are really the one in control.

Consider scheduling some time with a counselor or child psychologist to help you develop a behavior plan when your daughter's behavior stumps you. I suspect your child will test your control in other ways as she gets older. It's always nice to have a professional who "has your back" and can strategize with you.