I created a form before I had a Dropbox account. Can I upload from the form I already have to Dropbox or do I have to create a whole new form?

You can integrate any form with Dropbox, here is how to do so:

https://www.jotform.com/help/77-Upload-to-Dropbox-with-JotForm

Previously submitted forms will not be forwarded but any new submissions would be.  No need to recreate the form.