Hi Ally,
You are definitely not alone in being a child who grew up witnessing alcoholism at an age when you were definitely not equipped to handle it (in fact I am not sure any age is equipped to do so).
I think you may be scared for your cousin because you think that what happened to your mother might happen to her, but no two people are exactly alike. Also, your cousin may have to learn lessons for herself, maybe something will happen that will make her want to stop drinking, or at least only do it responsibly and when she is of age.
What you can focus on is just being there for her, so that way, if she ever does need someone to go to she will trust you as being a non-judgmental friend. It is hard for people who have witnessed sever alcoholism to not fear alcohol, but many people consume alcohol and enjoy it responsibly. I wish you luck, try going to alateen meetings where you will meet people your age who have had similar experiences. Try to align yourself with friends who would rather do other things for fun than drink. You are only 16 and you will never look back in life and wished you drank more at any age. I promise you that, so I think you are ahead of the game in seeing alcohol as not something that is enchanting but as something that can cause a lot of pain and hardship.
You're not alone. Good Luck!