Thank you for trusting your question to JA today. I am a licensed attorney with over a decade of law practice and over 20 years of experience in the legal field. I’m happy to be of assistance.
Unfortunately, there is no appeal process. You already know that, but you may not understand that gravity of what that means. There is no right to a military waiver. The waiver request itself is the appeal. To need a waiver, you already must be disqualified from service.
There is simply not a forum to raise a waiver denial on appeal. Waivers are being denied right now because the military doesn't need to use them to meet the staffing needs. This is because many are still trying to join due to the under employment in the civilian sector AND the military itself is shrinking due to enormous budget cuts. That means we have more people applying for jobs than we have jobs and waivers simply aren't needed to meet those goals.
Your only recourse is to allege some sort of discriminatory motivation beyond the medical issue (like your race, religion, gender, etc.) and then convince a civilian attorney to file a lawsuit on that basis. That is literally the only means of attempting to challenge the denial of a waiver.
If you have any further questions, please let me know. I invite follow up questions, so use REPLY for those. If you have no further questions then good luck going forward and please do not forget to rate my service with a top-three rating so that I receive credit for working with you today. Also, feel free to request me in the future, if you have questions concerning a different matter.