I currently have standard installed but have a license to Pro. Is there a way to type in the S/N to upgrade to Pro or do I have to completely uninstall and find the installer for Pro?
Yes, you have to uninstall Acrobat Standard first and then download/install Acrobat Pro. They both are two seperate applications and have different installers as well.
So, you can download Acrobat Pro XI from the below link and use the serial key that you have to serialize it.