Coming to this a bit late, as have been somewhat preoccupied with Christmas relatives etc. (urgh!)
I am another of those who suffers from depression and anxiety. These predate my drinking, so not surprisingly they haven't disappeared now I've stopped. But, and I sometimes forget and need to remind myself of this, things are so very much better. The depression dates back to my early teens and comes and goes. I didn't seek or get any help until my early 40s when the alcohol thing got really out of control, so dealing with it since has been starting from scratch really. Obviously not easy, but progress is being made which it never could be while I was in the very short term (hours) repressing it, and, in general terms, feeding it with alcohol.
I was in a vicious circle of drinking with anxiety. Extreme anxiety the day after I drank, which would lead me to drink to 'deal' with it etc. (It was a terrible day when I realized that a glass of wine at lunch time would mean I didn't have to suffer horribly until tea time, and a much worse one that I realized the same logic applied to first thing in the morning.) Obviously that sort of anxiety has gone. I no longer wake up on the morning with a jolt of anxiety. General anxiety (although to be honest I doubt it's ever really general. There is something subconscious going on usually, I suspect) Well, I have bouts of it still, and when I do I am, alas, thoroughly conditioned to think about drinking. Fortunately though, when I think about it further I realize that all I want is for the anxiety to go, rather than a drink per se. I am still reaching for my 'everything is alright' button. This is annoying, but not dangerous, on the whole. It's also lessening. And I hope will lessen further as I continue to recover.
The overall, I suppose message is that alcohol effects your brain chemistry. Take it away, and I think it's more than likely that you will recover. But obviously if there were issues that predate that you will need to address them, which it sounds like you are doing. Gosh, I have not said anything non-obvious at all, in fact

Recovery from alcohol is not an overnight thing, but it is fast enough for you to get really pleasant, gratifying moments of realization at how much better things are.
Holidays are notorious as relapse traps, but in a way they could be great opportunities to stop drinking as you are being taken away from your usual routine. I really hope you are having a good time in spite of the anxiety, Em.
Apologies for the cliches, but I hope not platitudes.
Rachelxx