As someone who has written many papers that have been published in reputable, peer reviewed medical journals and who has been a reviewer for several journals, I can tell you that it is not difficult to get a paper published.

All you need to do is write the paper listing your objectives, study design, analytical methods, results (including detailed data summary), and conclusions.

Submit the manuscript to a journal (for your subject matter, I would suggest a general interest journal like Journal of Pediatrics, the Journal of the American Medical Association (JAMA), or the British Medical Journal.

Once you have submitted the manuscript, the editor of the journal will send your manuscript, with your name and organizational affiliation redacted to ensure that your manuscript receives a fair review, to three or four reviewers (generally, recognized experts in the field).

The reviewers will offer suggestions, ask questions, and make a recommendation to the editor whether the manuscript be published as is, published with suggested modifications or answers to specific questions, or rejected. The editor will compile the comments and send them back to you so you can address the reviewers concerns.

Outright rejections only happen when the study design or conduct is not adequet to properly answer the question in the objective. Usually, the author is given the chance to address questions or misgivings the reviewers have before the final decision to publish with revisions or reject is made.

If you have proof, write the paper and submit it. If you can support your findings and address any concerns from reviewers, your manuscript will be accepted for publication.