Sweets. You didn't get yourself into this predicament overnight (including the Alcoholism) and you are not going to get yourself out overnight. Unfortunately (as with most addicted people including myself) we wait until things are in catastrophic meltdown phase and we have no other options before we take steps to turn things around.
The good new is that if you choose to stay sober and active in your own recovery, you will see things begin to improve. Your living situation, finances, mental/emotional state, confidence/self esteem, ect. will all start to improve. However it will not happen nearly as fast as you want it to and there is much difficult work ahead for you. The "carrot" is you have to believe it will get better. Don't give up. Do the work.
Then there's the "stick". I don't care how bad of a situation you currently find yourself in...if you begin drinking again to help relieve the pain, your situation will become exponentially worse. That is a 100% guarantee. You have two weeks invested in your sobriety and started working with a thearapist. Don't squander them. That is a very hard fought victory just to get to where you are now. Nobody in the History of Alcohol ever relapsed and then said later "That worked out well" or "I don't regret drinking again". Nobody.
Alcoholism always gets worse. Never gets better. Those nagging voices and thoughts in your head that are pushing their way to the front all the time, they do not have your best interests in mind. They are bald faced liars. That doesn't change the angst of having to listen to them all the time but you need to fear the consequences if you succumb to their suggestions to pick up a drink. It will not have a happy ending.
Keep looking for a stable and safe place to land (it can be very tough in NYC). You will find something.