An individual's "sincerely held" religious belief does not have to be part of a particular religions position on the vaccine to be considered a valid reason for exemption from getting it.
As long as you can articulate a well thought and reasonable justification for exactly why you hold your belief and how that relates to you spiritually, you have legal immunity from having to get it. No one else besides you gets to determine what your core beliefs are, nor how deeply you believe in them.
So I would very much recommend looking at some other people's exemption letter examples, then doing as much research as you can, write it up, and submit it for whatever you may need it for.
If after that anyone tries to retaliate against you, fire you, deny you service, you are well within your rights to sue them for discrimination. You can even look deeper into the topic over to verify these statements — should you be so inclined.
You're not required to attend a church or any other such thing for this stipulation to apply to you. In the US we have freedom of religion. This means a religion can essentially be anything that you can adequately explain that you practice and in which you hold your core beliefs. It does not state we have "freedom to specific religions approved by authoritative sources."
I don't know if this will help you with your situation, but I can at least promise you that you are protected by the law and you can sue the shit out of anyone who violates this as long as you took the time to present your "letter of exemption" to whomever it was that was trying to coerce you into taking the jab.
I hope this help, friend.