Telling your family is one tough thing to do. Each human individual is different, so each individual will react different to a confession like yours. But your family loves you, and I believe they will understand you. Of course, it can be a shock, but I am sure you will feel better afterwards, and that is what matters. And your family, especially your mom, can be a great support.
From personal experience I can tell you, as soon as you realizes that you are depressed, you can start to heal. Support from people you know will katalyse this proces.
I don't know you and I don't know your family, but my advise is just to let go of all those negative thoughts and tell them.
All the best!
Acceptance is the key
Existential depression and Insecurity
Try to keep smiling! :)