In the United States, a "terms of service" agreement is handled in the same way as a contract. The manufacturer has decided that anyone who uses the computer is agreeing to a contract with them, and schools can't force you to agree to a contract. Although somewhat counter-intuitive, the school can't compel you to use their computers unless there are no "terms of service" attached. If they try to you have grounds to sue.
In the United States a school can't agree to a contract for you. That's the law. How to handle this situation must be viewed in that context. The fact that a school official thought they'd agree for you isn't enforceable upon you. This is a feature of all U.S. contract law. Under U.S. law there are base expectations of how a contract works. They always apply absent a statute that changes them. The requirement is that the school have a law enabling the school to agree to a contract on behalf of the student and not the other way around. As for answering your question in any kind of a practical sense?
Put simply: Schools have responsibilities to listen to your parents, but most school employees and school board members won't care at all about a student's rights or opinions. If I were you I would be professional, I would have your parents very closely involved, and I would trust them to navigate this for me. There is a saying: "Those who can't do, teach." Although a lot of people mean to do good, often a school official or a teacher goes into the profession because they have baggage from when they were a student, and they want to get to be a petty Napoleon. When disagreeing with school officials you have to know your rights, you have to be able to cite laws at them, and you have to be willing to fight long and hard (including filing a lawsuit if necessary). If your parents are not willing to fight for you then you will probably wind up resigning yourself to representing your own children better some day.
A "terms of service" document is handled by the courts as a contract. (For more information on this, see the Computer Fraud and Abuse Act. This is very well-settled law. Using the computer implies that you agreed to the contract, but you have ways out of the contract if you object when the contract is actually being enforced.) Since other answers didn't seem to know how the law works, let's point out a couple of the fundamental parts of contract law as well.
Contrary to common belief, with the singular exception of your parents, there isn't anyone that can agree to a contract for you. Not your school, not your teacher, not any specific school official. The legislature of a state government and the state's school district do not have the same level of authority, and internal policies can't compel your participation in a contract. Contrary to common belief, there is also no such thing as agreeing to a contract law "by default" unless you're an adult who is making a choice to participate in an activity that is optional for you. You are under 18, and you are not participating in an optional activity. The idea that you could be "forced" to agree to a terms of service is a lie. Whoever at your school tried to tell you this was more focused on making their own job easier instead of obeying the law.
That having been said, the sad fact is that most of the time your personal information isn't going to be protected by statute. Your school will probably try to lean on one of the few proactive things they get to do: They have a legally-recognized authority to maintain order, which is not supposed to apply here, but a lot of incompetent individuals like to act like that means they can do whatever they want. Schools have responsibilities to listen to your parents, but most school employees and school board members won't care at all about a student's rights or opinions.