For security and privacy reasons, school resources need to be managed by a work or school account (email). For that reason, please make sure you either change your email for Kahoot! to the school's email or keep your original Kahoot! account and move / share your Kahoot! games to your school account Kahoot!
It is not possible to merge accounts but you can duplicate the kahoots from one account to have them stored on another account very easily.
First, you need to make the kahoots public: https://support.kahoot.com/hc/
Second, you need to log in to the new account (the one on which you want to have the kahoots stored), find the kahoots in the Discover section by searching for titles/username of the author, and duplicate them: https://support.kahoot.com/hc/
You can update your email from your account menu.
In short, all you need to do is:
- Log in to your account,
- Click on the account's avatar in the top right corner of the screen and select the "Settings" option,
- Select "Edit Profile" section,
- Update the email address,
- Click "Save".
You can also find an illustrated help article here.