Yes, your parents will be able to link your school account to their family. Or if you have a child account under a family you will be able to request to join your school, here is how.
This will allow you to use the one account both at home and school. You will only need to use one username and password.
You will be able to earn coins for that account and you will not lose any of your progress or have to start over.
Here is how your parents can add your school account to their family.