This may be a slightly unpopular opinion, but I believe it is worth stating. Disclaimer: This thread is regarding vaccination requirements for entrance to a service academy. I am responding to that alone. I am not addressing the effectiveness of the shot, the public mandates, ect.
First, it is important to note that you are not even at the start of your career. You are trying to enter a four year evaluation period that will hopefully get you to Day 1 of your career. This is not meant to demean you, I was there once. As someone who has been there, done that, got a bunch of time flying Vipers across several continents plus a trip to the Sandbox, I am trying to give you SA on how the military works.
Here is my opinion, and I am breaking it down into the two main points you have brought up. Your first point is the risk of side effects due to family medical history. First, I am sorry to hear about your mother and I hope she is doing better. That is a difficult position to be in. I understand your concern especially considering your back up career. Here is the first unpopular opinion I will say. The military does not care. It can not afford to care. You are going to have to do your own risk assessment, weigh the potential risk vs. your desire to enter the military, and make an informed decision. The military will not waive requirements when you do not have your foot in the door yet. I have several friends who were kicked out of ROTC for very mild eczema. Would it have impacted their career at all? Not a bit. However for medical issues before commision, it is black and white. Just like the requirement to get the COVID vaccine.
This ties into my second point. You say that each case should be handled on a case by case basis. This is not how the military works. I am not ridiculing your perspective, but the quicker you understand that you are four years away from being a very very small gear in the machine of the Air Force, the more things make sense. One of the wisest IP's at my B-Course sat us down at the squadron bar one day and told us, "We are not special. We are numbers. Expensive numbers, but numbers all the same. We are all replaceable. Never forget that". Once you get in and start having more invested into you, you have slightly more weight to request waivers. You aren't there yet. Additionally, the COVID vaccine will not be one of those waivers due to a simple fact. You need it to deploy and be stationed overseas.
I am a FIRM believer that if you can't deploy, you should not be in the military. This requirement is due to host nation guidance. Many countries will not allow service members in if they are not vaccinated for COVID. As sovereign nations, they have the right to dictate those requirements. Potentially America's greatest strength is our network of overseas bases. If you can not go to these bases, you are now a gear that is slowing down the machine.
This response might have been lengthy, but I hope it provides insight to those who read it. Regardless of individual feelings regarding the vaccine, this is, and will remain to be, a black and white entry requirement.