Can you access your email via web browser? Most, if not all, POP email accounts nowadays can be accessed by web browser, in addition to be retrieved with an email client such as Microsoft Outlook. If you do not know whether you can access your email by going to a website to view it, we can help you determine that if you tell us what email service you are using.
Based on what you have told us, you are getting those old emails downloaded again because they still exist on the mail server from which Outlook retrieves them. Normally, if a POP email account, which your comments indicate you have, is set up in Outlook or some other email client/software, Outlook (or other ...) tracks what emails have been downloaded and communicates with the mail server to avoid duplicate downloading of messages. This is how the process works unless the user sets Outlook to delete emails from the server once they have been downloaded. This tracking data got destroyed when you deleted the old .pst file. So, when you start using Outlook again, it no longer knows which emails were previously retrieved and, therefore, starts from the beginning. Assuming you can access your email account via a web browser, you could do so and then delete all the old emails there. Then, you could resume using Outlook and it will only be able to retrieve new email messages because the old stuff no longer exists on the mail server.
Alternatively, you could change a setting in Outlook to tell it to delete emails from the mail server once they have been retrieved, i.e. downloaded to Outlook, retrieve all email, and then do a one-time cleanup of your emails in Outlook by sorting them in date order and deleting all old messages you no longer want.
