Outlook 2003 DOES have a limit of 20GB, and you shouldn't begin receiving warnings until you hit 18GB. If you are using an older PST version (pre-Outlook 2003) and have already migrated that data into your Outlook 2003, I would suggest you do go ahead and create a new PST and re-import it on the account.
You may find this link useful:
Migrating older .PST files to Microsoft Outlook 2003