To update your LinkWhisper plugin there should be an auto-update in the WordPress dashboard. So, you would just click "update" when an update appears for the plugin in wordpress.
You can see the updates by going to "Dashboard" > "Updates". Or you can go to "Plugins" and scroll to find "Link Whisper", you will see an update link if an update is available.
If the link or auto-update isn't showing you can download the newest version from your Linkwhisper account:
And enter the login information for your account. If you don't know your login, it's the email you used when you purchased. Then just click "forgot password" to receive your login password.
Just remember to delete the old plugin, and then reinstall the newest version. (All of your settings and links will be saved when you delete and re-install the new version).