I tried writing 2 letters coming out as both lesbian and possibly genderfluid transmasculine but I could not word it the way it sounded in my head so gave up. I actually have a learning problem where what I'm "writing in my head" it doesn't come out the way it sounded in my head. Plus the letter sounded rude so yea not the right way to do it for me but I'm scared to talk to them face to face at first. I tried contacting ingredients out at 14, didn't go so well.
That problem of a disconnect between what you imagine and what you produce is somewhat common I think. It's helped by writing out whatever it is you feel is good at first, then re-reading it and seeing where you went wrong. Several sessions of doing this and you'll come out with a fairly polished letter. That's also quite a lot of stuff to come out as in one letter if you're not confident in your writing. How did you phrase it? You could start by saying you've felt weird for some time and finally found a word for what it was. Regardless of how "good" your letter ends up being, as long as its clear and heartfelt, I'm sure the intended readers will get the message. Don't be discouraged.
Also don't try and edit it right away. Take a day or two, then go back and reread it. Make corrections after a bit of a break. Its how I work on my stories, write a chapter, then go back and edit it usually a week later.