If i have anxiety and depression as a teenager, is it normal to begin drinking to make me feel better?

No: It is not uncommon to develop substance abuse issues as a maladaptive coping mechanism. These tendancies are not healthy and can be avoided by proper therapy early on.

People do it: If you feel that "normal" is simply what a lot of people do, then drinking alcohol to cope with anxiety & depression is "normal." but it isn't helpful or healthy in the long run! adding alcohol to this just brings in another layer to deal with. I'd suggest being "abnormal" and insightful instead . . . And seek treatment for your anxiety and depression from a professional.

Not normal, common: It is not normal to resort to alcohol to deal with anxiety and depression, but it is common. Self medication with alcohol will only lead to further problems. You should see a psychiatrist and get proper treatment and management of your feelings.