Just because you're feeling sad, does not always mean depression - always go to a doctor to check.
Try to calmly explain to her the difficulties of depression and perhaps show her some things about it on the web. Sitting down and talking about it mostly helps and show her how hard it has been for you. Perhaps you could talk to someone at school about it, too, like a school counselor or a best friend. It's always good to get things like this off of your chest.
But go to a doctor so you can get diagnosed too, she can't deny it then and the doctor will give you things (tablets or therapy) to help cope wit the sadness.
If you don't want to get out of bed because you're afraid someone is going to drop dead, that's a whole different issues all together. That's not depression. I'm sorry that you have to go through that, and that is definitely a concern for you to talk about with a trusted adult. But self diagnosis is almost never correct, on any mental illness or disorder. You know yourself best, but you should leave it to the professionals to guide you through it.
I live with my dad & he always threatens to take my mom to court for child support. but my mom is barely making it own on her own. I wish I could live with my mom because she knows how to have fun.
-southern born and raised-