Hi Addmik!
You can have both problems at the same time.
If you develop the habit of medicating your anxiety with alcohol, alcohol first becomes your main coping mechanism, then your only one, then your addiction. (If that hasn't already happened.)
I suggest you continue to cut out the alcohol completely and try to deal with your anxiety in a healthier way. Then, either you won't want to drink anymore -- or you still will, and you can ask yourself then, is alcohol a problem for you on its own?