Glad you came by with your experience . . . I cannot speak from direct experience with either drinking or the meds that you are taking, however, a close personal friend, had a similar experience. She also was drinking as much as you were if not more along with smoking 2-3 packs of cigarettes a day because of anxiety triggered by marital situation. She also started on meds and experienced a substantial decline in the alcohol consumption to the point where she now drinks a couple of beers on some weekends and often goes long stretches without drinking at all.
So, to answer your question, you might drink because of the anxiety and, for you, the alcohol appeared to decrease your anxiety (this is a bit of a false reality because once the alcohol wears off, you can experience rebound into deeper anxiety, etc.).
What I would view this as is a second chance to get away from drinking as much as possible and perhaps look at what triggers your anxiety. If you have had anxiety all your life, sometimes a bit of directed counselling would guide you to understand and deal with your triggers. . . .because, you do not want to return to anxiety and drinking should you decide to stop your meds . . .
In any case, I am pleased that you are finding relief from your anxiety and yes drinking is often a coping mechanism for anxiety . . . whether the effects of the meds will wear off, that is a difficult call because everyone reacts in a different fashion . . .but, if you feel that you are drinking more, then get to your prescribing doctor . . . .to enhance the meds, though, look at your lifestyle also in terms of exercise, sleep, diet, etc. as you may be able to do something to prolong the good effects of the med or make changes that will contribute to your managing anxiety long term.
Do let us know how you are doing and thank you for sharing your experience . . . if we can do anything to support you in your recovery, please let us know . . .take care, kc