You have asked a very good question. It’s probably a question that many teenagers and parents have pondered. To give you the best answer I would need to interview you. My questions would be geared toward determining the seriousness of your symptoms. I would want to know information such as how frequently the symptoms disrupt your life, to what degree and whether you have contemplated or attempted suicide. Your answers to those questions could help me to determine whether you have depression.
From what you have written, it does seem that your symptoms are significant and concerning. Having extreme mood swings is not normal. Many individuals will occasionally experience periods of irritability but it’s unusual to have “extreme” mood swings.
You mentioned feeling hopeless and worthless. You didn’t specify how often you feel that way. Teenagers especially may experience those feelings occasionally and that may be relatively normal. To experience them on a regular basis (a few times a week) would be abnormal. You also feel that you can’t control anything. I am not certain what you meant by that expression but usually that feeling is associated with anxiety. Depression and anxiety commonly co-occur. I wonder how often you feel out of control and if you have a reaction to that feeling.
I tried to provide a nuanced answer but the simple answer is this: If you feel depressed then you should seek help. It’s not advisable to let your depression symptoms worsen before you decide that treatment is warranted. It’s better to be proactive and treat the symptoms as soon as you notice them occurring. You already have a letter written to your mother. The next step would be to give it to her. It is important that she knows how you are feeling. Please take care. Thanks for writing.