Is my form public? I only want it to be seen on my website.

Since the URL of your JotForm is public, it may be accessed by its URL outside of the website. However, it may be hard to access outside the website if you can embed the form using source code embed method. Please refer to the following guide that can help you in getting the source code for your JotForm.

https://www.jotform.com/help/104-How-to-get-the-Full-Source-Code-of-your-Form

Hope this information helps!