As stated no one can tell you definitively here. I can tell you almost anything is possible in regards to waivers. I'm missing a kidney that was taken out due to a wilms tumor that also metastasized in my lungs (requiring removal of a segment). There were a number of other surgeries and conditions that I was casually told would require waivers as well. In reality the missing kidney was the only condition that required a waiver.
When I applied to the service academies and for ROTC scholarships straight out of high school I was told a waiver was required and the process took over a year to obtain a waiver. I also went through a different waiver process at the AF Academy for rated aviation positions. Last when I separated from active duty and started HPSP for some reason I needed to go through the entrance waiver process again but this time it was much quicker (probably my job in the AF at the time helped). I'm also assuming after HPSP I'll go through another waiver process before I enter active duty again.
In regards to the missing kidney waiver my nephrologists was a former AD AF provider and was in the reserves. In addition to labs and the typical clinical documentation he wrote a memo that highlighted my active lifestyle (the sports I played in HS and the times that I ran). It may sound stupid but if you read the DoD instruction you'll see a lot of the phrase that prevents "physically active vocation in civilian life" and if you can show that you are very active and would not be limited by your condition it can only improve your chances.
In regards to your murmur, from my understanding the murmur isn't what will require the waiver it's the cause of the murmur so hopefully your providers have determined the cause of the murmur. Check out DoDI 6130.4 go to the heart section and you'll see no mention of murmur but you'll see valve/heart/vascular defects that often cause murmurs. You'll see some are ok, some require waivers and other causes will not be found in the document (waiver not required but additional exams to verify this is the actual cause will likely be required).
That being said you're going to need to really pursue this waiver it won't come easy or fast and no one will walk it through the process unless you do. Basically keep copies of everything you do and submit. If you don't hear anything for extended periods of time (months) which will occur don't be afraid to write letters or call. They probably will just tell you your case is being reviewed, but if something is missing or lost they may let you know. My opinion is if you're not serious about obtaining the waiver you won't get it if you are serious you have a chance.
