If you've registered at grammarly.com instead of grammarly.com/edu, you need to log out by going to app.grammarly.com and clicking Log out in the left-side panel, then log in at grammarly.com/enterprise/signin. Then, find the email "ACTION REQUIRED: Confirm your email" in your inbox and click Verify email. If required, enter the access code provided by your institution.
Alternatively, you can delete the account you created by mistake by following the instructions described here. After that, go to grammarly.com/enterprise/signup to create a new account.
See I Signed up at Grammarly.com