List organization on individual profile signup
You can add a Contact Reference field (one of the types of Custom Fields that you can create) and then display that in your profile and limit that to just the group of schools. users need to have permissions to use the autocomplete option so you need to visit /wp-admin/admin.php?page=CiviCRM&amp;q=civicrm%2Fadmin%2Faccess%2Fwp-permissions&amp;reset=1 and find th permission "CiviCRM: access contact reference fields 
Allow entering data into contact reference fields" and give it to your anonymous visitors. (You may also need to give "CiviCRM: access AJAX API 
Allow API access even if Access CiviCRM is not granted")

The above won't do this as a Relationships, which is the ideal, but I don't know how that is done via Profiles for WP