If you are not married and the case is a paternity case then all filings do not show up on the register of actions. no one can access them.
Paternity actions are confidential and the general public does not have access to the pleadings. I don't think you will serve any purpose throwing information out to the press, that is more or a vindictive attitude rather than a let's figure this out attitude.
Note this answer does not constitute legal advice, and should not be relied on. Each situation is fact specific and court specific, and it is not possible to evaluate a legal problem without a comprehensive consultation and review of all the facts and court pleadings filed in the case. This answer does not create an attorney-client relationship
Paternity files are not considered public records and therefore are accessible only to the parents and/or their attorneys.