(((((((((brighteyes))))))))))))
I think it's very brave of you to tell your mom about what's going on. I was terrified when I did it. I guess the only advice I would give is to remember that your mom loves and wants what's best for you. People's reactions to depression differ as much as the people who suffer from it, so just try to explain everything as clearly as you can. If you think the letter would explain it best, then by all means use it. I know I'm better at getting my thoughts organized on paper.
On the off chance that you change your mind and don't want to talk to your mom, what about a school counsellor? They're confidential and could either help you come up with the words to tell your mom (you could probably arrange a meeting between the three of you if you'd be more comfortable with that) or could steer you in the direction of further help. No matter what you do, I hope you sit down and talk to someone about how you've been feeling. Depression is highly treatable and seeking help from family or a professional is going to go a long way in getting you past it.
Sending lots of hugs.