After one person has voted to close as a duplicate or one person has flagged as a duplicate, here is what happens:
- the original poster (only) sees a notice that this might be a duplicate, and can agree or disagree.
- the post is added to the "close votes" queue where other users can vote to close or to leave open
If at any point the post is edited, it is added to the "reopen queue" where other users can vote to reopen it. If it is closed as a duplicate before it is edited, high rep users can vote to reopen from the post itself, which will also add it to the reopen queue.
Assuming your edit made it clear that it is not a duplicate, over the next little while either the close votes will age away, or enough leave open votes will be left, or (if it was closed) enough reopen votes will be left, that the post will be re-opened if it was closed, or will have the notice (that only the original poster saw) removed. At this point you will have successfully removed the duplicate-ness of the post. It's really a matter of time.