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I'm sorry to hear that you are going through all of this! The reason your school told your parents is because they are mandated reporters, at least if you live in the United States. This means that they are required to tell your parents if you are doing things to hurt yourself or other people. You should still be proud of yourself for reaching out, because that is the first step towards you getting help.
Do you think it would be easier to write your parents a letter, or would you rather tell them in person? Some talking points may include asking them to not tell anyone else, because this is a personal matter that you don't want everyone knowing about. Say you would really appreciate it if this could stay between you three. I can't say for sure whether they will search your room or your body. My parents would examine my arms and thighs when they found out about me, and I will say the only thing it accomplished was making me learn how to hide it better. Maybe you can make a compromise with them, such as giving them your self harm tools so they feel more comfortable with not searching you.
Another thing you can tell them is how they can help you. Is there anything they can say or do that will make things easier on you? They're worried about you so maybe knowing how they can actually help you will ease their minds a little bit. Maybe explain a little about why you self harm and what is triggering the eating disorder and suicidal thoughts. You don't have to go into extreme detail if you're not comfortable doing so, but it again may help them understand a bit about what you are going through and some of your triggers.
Telling them can also be the first step in getting help. I don't know how things work in a boarding school setting, but maybe they can set you up with a therapist, or at least set up weekly appointments with a guidance counselor or other school staff member so you have someone to talk to on a regular basis. Sometimes it can really help to have someone unbiased to talk to about your problems and what is going on.
This is our link to alternatives and coping mechanisms. Some of them may be useful for you in avoiding self harm and other things.
I know it's scary right now, but you can get through this!