Both Free and paid versions offer the same basic protection. So, not likely a license upgrade will solve the trojan infection on the other computer.
You could upgrade after using a Windows license purchased using the Mac, and paid does offer additional features that will offer protection in areas Free does not for the future, but best to submit logs for the malware expert to clean and diagnose the system infected. Cleaning your system first is priority.
https://forum.avast.com/index.php?topic=194892.0 Attach logs in your next reply; use
Attachments and other options below the Reply box to do so. You should have three (3) logs attached when done.
A malware expert will be contacted as soon as possible once this is done.
Downloading and installing free stuff is often a source of infections.