I'm sorry that I wasn't clear. I use Zotero in my university Google docs. However, the university is closing its Google apps. When I try to use Zotero in my personal account google doc, I get this error message: "The Google account you selected does not have permission to edit this document. Please try again, and be sure to choose the account with editing access."

That error message doesn't have anything to do with your Zotero account. You just need to choose the Google account that actually has access to the document. If you've transferred the document to your personal Google account, that's the account you'd need to choose. If you haven't, you'd have to do that first, independently of anything related to Zotero.