A 16 year old loves and needs their mother desperately. They just don't show it.
What support do you have for getting sober? I enlisted my doctor, and posted frequently on SR.
Try working as sobriety like you would for an exam. Read about the damage it does to your body and mind. Write out your idea of where you'll be in 5 years if you don't stop. Picture yourself sober, successful, fit, healthy.
It took me a few months from when I really wanted to stop, to the time it became possible. When finally I quit I was convinced I would succeed because over that time I gained motivation until something just clicked.
It also helped me to have a goal (one year) to work towards. Once the year was up, no way was I going to drink again because I like my life way too much.
Don't give up; keep working at it, and don't expect it to be easy. Earn it.