I want people filling out my form to be able to upload a song or video. Is that possible?

Yes it is possible. 

You can achieve that by adding File Upload field to your form. Inside of this guide you can find how to create a file upload form: https://www.jotform.com/help/332-How-to-Create-File-Upload-Forms 

You would also need to allow extensions for formats that you want to accept:

How to Change the Allowed File Types/Extensions in the Upload Field

And you will need to increase the file upload size limit of your upload field:

Changing the File Upload Size Limit

However considering that you have free account, please note that for free account available account upload space is 100 MB.

More about different account types and limits you can find on our pricing page. 

Hope this will help. Let us know if you need further assistance.