If you created your account with your ohio.edu email, you should see it listed in the email settings. We recommend you include a personal email account to ensure you retain access to your Zotero account, but only the ohio.edu email is required to get the unlimited storage. If you want to add a second email, enter the email and click the button labeled "add".
Verify the added email by following the verification instructions (check email account for verification email form Zotero).
If you want to check if you have unlimited storage, visit the storage settings: https://www.zotero.org/settings/storage. As long as Ohio University subscribes to an Institutional Subscription AND you have an Ohio.edu email associated with your account you should see a message of Unlimited Storage.