Postcard1 bless you
Definitely the best and only way to make amends is to stay sober. As others have said, actions speak louder than words.
Check your expectations too if you have any, that is, of sending the letter. I know that when I've done similar, the very obscure - even to me! - intention was that it would change how my partner felt. It didn't. But staying sober, and building a life, that does.
Wish you well