If your platform (premium url shortener or premium media script) do not send any emails then it is most likely your server cannot send emails. You can try the following solutions to fix the issue.
1.0 Add SMTP Information
Add SMTP information in the admin panel > settings > SMTP or Extra Settings. Make sure you have the correct username, password and port number otherwise it will not fix the issue.
2.0 Change Default Email
If adding your SMTP info does not fix the issue, you need to change your default email address as some hosts do not allow you to send email from @gmail.com or @outlook.com. They require you to send an email from @yourdomain.com. In this case go to admin > settings > general settings and change your email.
3.0 Make sure SMTP port is not blocked
Sometimes, especially with managed VPS, SMTP ports might be blocked by default. This will prevent the product to connect the SMTP port hence preventing it to send an email. If the other solutions do not fix the issue, you need to check if the port used is not blocked by your firewall.