You already own the copyright to any photograph taken by you (unless it was taken in the course of your employment, in which case your employer would own the copyright). There is no need (and, indeed, no method) for registering that copyright.
By submitting your photograph to the newspaper (when no offer of payment has been made) you're clearly granting the newspaper the right to publish that photograph without payment. However the copyright remains with you and the newspaper can't provide copies to other people without your permission. (Our local rag put a reference number against their own photos, so that copies can be ordered. But photographs like yours are simply labelled as 'contributed').
Chris