With all the students using the same account, Record Level Access control isn't very doable as you have no easy way to identify each user. Unless each student uses a different device and only that device to access the DB, you now have no automatic method for identifying who is who and thus who has access to what records.
Here are some options to consider.
a) give each student their own account. This can be automated with scripts to reduce the "chore factor".
b) Take each new user to a screen each time they open the file where they enter a unique identifier into a global field before they can proceed which you then use to control access via Record Level Access control and in scripts. This essentially drops in place your own much less secure system of access control.
c) set up an interface where they students do not see any records when they first open the file and can only pull up records they identify as theirs (not much different than b) really) a script can perform a find or use a relationship to access only their record(s). A custom menu (FileMaker Advanced) that does not allow "show all" or "show omitted" would be used with script triggers on Mode change that kick in an omit records from any finds that don't belong to the current student... or a layout that consists only of global fields (where scripts move data in and out of the global fields) can be used to present the data to the students on this layout (FileMaker Advanced not required for this).
A simple fix is to have the on form load script trigger or record load script trigger to create a new record if the user is using the guest account, then anyone using the guest account can only create a new record and not see any other records.
Remember to hide any navigation buttons or hide and lock the tool bar to stop them finding another way to previous records.