Is it possible to turn an existing form into an encrypted form? Or do I need to create an entirely new form?

Yes, you can turn on Encryption for the existing form. Please navigate to Settings > Form Settings > Show More Options then scroll down to Encrypt Form Data and set the field to Yes. Then follow the steps in this guide: How-Can-I-Enable-Form-Encryption

For more information, you read these articles: Encrypted-Forms-and-How-to-Use-Them