Your hair is tied with a headband, which means you are in control. Once the headrope is broken, the hair will spread out irregularly and get out of your control. This is also related to your exam dream. You have recently estimated that something really bothers you and needs you to take it seriously.
There is another explanation for dreaming about exams. When I was a child at school, my parents, teachers and other elders would supervise me and criticize some of my behaviors, especially the exams. The elders always comment. Since you have stepped into social work, you can't get the moral comfort of condemnation by passing the exam, so when you are doing something wrong or not completing something perfectly, you will dream about the tension during the exam, in order to make your conscience feel better and get a psychological balance.