That sounds a lot like my own internal dialogue regarding my mom (and dad), who were both alcoholics when I was growing up and living at home. I think it's well and fine to say exactly what you said here:
the way she behaves when drinking makes me anxious, tense and upset? That I worry about the way she drinks and that I don't like who she becomes when drinking
However, from my experience.. it wont change anything. It might make you feel a little better, but it might not, especially if she pulls the martyr role (my mom would do the same) and becomes upset, and continues to drink as normal.
In alanon (I haven't gone..), you learn how to establish boundaries, to protect yourself from the active alcoholism of loved ones. It's super complicated since you live with her, and I hope you have a plan in place for that to change as well. Mostly it's up to taking charge of your own self care, and your new recovery. Finding support outside of your family, and among other recovering alcoholics or professionals experienced in working with us.
I remember those "talks" with my mom all too well. I cried, I threw things, I threatened to never speak to her again.. nothing made a difference until SHE had enough, and thankfully she (and my dad) got sober when I was around 19 years old. I became an alcoholic, and didn't achieve recovery until I was 34, but I *still* carry around the effects of their alcoholism.