You're 16 and have a passion for music. I was there. In your exact situation, except maybe not as dedicated as you at the time. Do not do music for the money. I don't. I have gone in with the mindset of, I am going to make this happen. This is what I love. So, I have decided that whatever I do, even if it means not living as comfortably as some, I am going to work in music.
Why? Because it makes me happy. I love it.
If you want to live a comfortable life, music is probably not a good choice, but if you love it and cannot see life without it being your career, do it. That is where I am right now as of 22.
My parents never thought it was a good idea. We fought some battles over it, but I earned a full tuition scholarship to pay for my school, so I chose to major in music. They knew by that point, that I was serious and not going to change my mind. They knew that I would do it even if they didn't want me to. So, they got behind me and supported me.
So, my advice to you (if you do decide to do music) is to keep working hard at it, and show your parents that you are serious. They may be writing it off as a phase. Anyway, let them know that this is what you choose, even if it means doing it yourself without their help.
They may get behind you and support you, or they may not. I don't know. But, if you cannot live life in another career then you do not have a choice.
My dad and I were eating the other day and talking about music. He told me that he was proud of me with tears in his eyes. He said that no matter what he knew I would be doing something I loved. That meant the world to me.
Sorry long story, but hopefully it will give you some encouragement. I don't know if I will ever "make it" in music, but I know that I will be working with it for the rest of my life.
EDIT: PS - Never expect anything to just happen for you. Have initiative. Get out there and make it happen. Blood, sweat, and tears.