Whilst by default, Blogger is an open forum, it can be locked down if you are wanting to limit visibility. Here's how.
1. Make sure you are logged in to your school google account (ideally in Chrome).
2. Open a new Tab and type in blogger.com. That opens Blogger in management mode.
3. Since you can have more than 1 Blog, go to the Blog you wish to 'lock down'. In "Settings" choose, "Basic", then you can explicitly specify the authors and the readers.
You can share it to a group BUT if the group has not been set up to accept emails from members outside the group, they will never get the notification.
This means you cannot share these to your student groups. They are all closed groups.
The only way a person can join this Blog is to find your invitation and follow the prompts.